Finally could reproduce.  The problem was that on a metadata reset 
(e.g. a day change), we were not converting the thread object into a 
Hash object on the initial reset.  Thus, the behavior was only 
manifesting itself when the mailbox changed after the metadata reset 
(e.g. deleting a message; new message in mailbox).  This was causing a 
JS error that caused ViewPort.isbusy to remain true indefinitely, 
causing any future ajaxResponse() calls to fail.

Very weird that no JS error appeared for you.

Changes have been made in Git for this ticket:

[mms] Fix issue in dynamic mailbox view with thread sorting and a 
reset of mailbox metadata (Bug #10835).

  3 files changed, 19 insertions(+), 15 deletions(-)
http://git.horde.org/horde-git/-/commit/a4ca1f507d882c09eac30c7d16d1dc54e5c308fa

I went ahead and manually tried to reproduce by changing the local 
system clock, and I still can't reproduce.

Next, changing to a different mailbox, the UI shows Loading... but 
nothing happens, not even a request, or at least none that's tracked 
by firebug. No JS error either. Some mailboxes load, others don't. 
Some load but aren't displayed.

Examples of post-midnight communication that fails:

deleteMessage, request:

cache        {7}SU5CT1g247464,247471,247646,247784,247802,248423,248541,248859,248903,248909,249083,249099,253916,254177,254525,254752,255594,255678:255679,255759,255798,255806,255869,255897,255918,255973,256149,256152,256829,257040,257188,257193,257201,257243,265461,265913,266055,266116,266187,266336,266341,266376,266429,266471,266482,266635,266692,266701,266720,266746,266793,266816,266861,266867,266924,266966
cacheid        V968256253|U266968|M171|9|1|D121011
slice        1:56
uid        {7}SU5CT1g266746
view        SU5CT1g

response:
{"response":{"ViewPort":{"cacheid":"V968256253|U266968|M169|9|1|D121011","data":{"247363":{"flag":["\\seen","personal"],"mbox":"SU5CT1g","uid":247363,"size":"4 KB","date":"18.09.2011","from":"PEARBug Database","subject":"[PEAR-BUG] Bug #18817 [Opn->Fbk]: Incorrect rendering of Function 
rule"}},"metadata":{"readonly":0,"thread":{"266924":"","266861":"","266867":"3","266816":"4","266793":"","266966":"3","266720":"4","266701":"","266692":"","266429":"","266376":"","266336":"","266482":"03","266471":"3","266187":"","266635":"3","266116":"2","266055":"","265913":"","265461":"","266341":"0003","257243":"003","257201":"03","257193":"3","257188":"","257040":"","256829":"","256152":"3","256149":"","255918":"3","255897":"","255869":"","255679":"","255678":"","255806":"3","255798":"2","255759":"2","255594":"4","254752":"","254525":"","254177":"","253916":"","249099":"","249083":"","248909":"","255973":"3","248903":"4","248859":"","248541":"","248423":"","247802":"","247784":"","247646":"","247471":"3","247464":"","247363":""}},"rowlist":{"266924":1,"266861":2,"266867":3,"266816":4,"266793":5,"266966":6,"266720":7,"266701":8,"266692":9,"266429":10,"266376":11,"266336":12,"266482":13,"266471":14,"266187":15,"266635":16,"266116":17,"266055":18,"265913":19,"265461":20,"266341":21
,"257243":22,"257201":23,"257193":24,"257188":25,"257040":26,"256829":27,"256152":28,"256149":29,"255918":30,"255897":31,"255869":32,"255679":33,"255678":34,"255806":35,"255798":36,"255759":37,"255594":38,"254752":39,"254525":40,"254177":41,"253916":42,"249099":43,"249083":44,"248909":45,"255973":46,"248903":47,"248859":48,"248541":49,"248423":50,"247802":51,"247784":52,"247646":53,"247471":54,"247464":55,"247363":56},"totalrows":169,"view":"SU5CT1g","rowlist_reset":1,"disappear":[266746]},"poll":{"SU5CT1g":0}}}

behavior:
message is striked through but not moved to trash (in the ui, it's all 
fine on the server). Or maybe not? Loading the same mailbox again, the 
message is still marked as deleted (striked-through). viewPort Response:

{"response":{"ViewPort":{"cacheid":"V968256253|U266968|M169|9|1|D121011","data":{"247363":{"flag":["\\seen","personal"],"mbox":"SU5CT1g","uid":247363,"size":"4 KB","date":"18.09.2011","from":"PEARBug Database","subject":"[PEAR-BUG] Bug #18817 [Opn->Fbk]: Incorrect rendering of Function 
rule"}},"metadata":{"readonly":0,"thread":{"266924":"","266861":"","266867":"3","266816":"4","266793":"","266966":"3","266720":"4","266701":"","266692":"","266429":"","266376":"","266336":"","266482":"03","266471":"3","266187":"","266635":"3","266116":"2","266055":"","265913":"","265461":"","266341":"0003","257243":"003","257201":"03","257193":"3","257188":"","257040":"","256829":"","256152":"3","256149":"","255918":"3","255897":"","255869":"","255679":"","255678":"","255806":"3","255798":"2","255759":"2","255594":"4","254752":"","254525":"","254177":"","253916":"","249099":"","249083":"","248909":"","255973":"3","248903":"4","248859":"","248541":"","248423":"","247802":"","247784":"","247646":"","247471":"3","247464":"","247363":""}},"rowlist":{"266924":1,"266861":2,"266867":3,"266816":4,"266793":5,"266966":6,"266720":7,"266701":8,"266692":9,"266429":10,"266376":11,"266336":12,"266482":13,"266471":14,"266187":15,"266635":16,"266116":17,"266055":18,"265913":19,"265461":20,"266341":21
,"257243":22,"257201":23,"257193":24,"257188":25,"257040":26,"256829":27,"256152":28,"256149":29,"255918":30,"255897":31,"255869":32,"255679":33,"255678":34,"255806":35,"255798":36,"255759":37,"255594":38,"254752":39,"254525":40,"254177":41,"253916":42,"249099":43,"249083":44,"248909":45,"255973":46,"248903":47,"248859":48,"248541":49,"248423":50,"247802":51,"247784":52,"247646":53,"247471":54,"247464":55,"247363":56},"totalrows":169,"view":"SU5CT1g","rowlist_reset":1,"disappear":[266746]},"poll":{"SU5CT1g":0}}}

Did you clear your browser cache/viewport after updating.  Things 
would have been badly broken if using a viewport with old cached data 
and applying the above patch.

As previously mentioned, especially regarding the sort resetting - 
this would be exactly the symptoms of the issue that would be fixed by 
this commit.

I can manually change the day and I see no issues.  To simulate the 
changing of a day, overwrite the date('mdy') strings at 
IMP_Mailbox#_getCacheID():line 1466 and 
IMP_Views_ListMessages#listMessages():149 to the same string (that 
doesn't correspond to today's date).

This is exactly the commit that I mentioned that made things worse for me.

Almost positive this was fixed last week by this:

commit 6f435e07cd2a1419a35c1de8f73fa81cc3d22b9c
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Wed Nov 30 15:21:56 2011 -0700

     Fix regressions in search mailboxes due to Ticket #9773

     Move UIDVALIDITY check before empty mailbox check, since a UIDVALIDITY
     failure should cause all viewport information to be reset, regardless of
     whether the mailbox contains messages.

     UIDVALIDITY will also fail when the day changes, so metadata creation
     needs to appear below this line since metadata will be reset in this
     instance.

Prior to this commit, the metadata was being improperly updated which 
exactly fits the symptom of arrival sort becoming the sort method in 
the mailbox.

FWIW, I can't reproduce.

There had been issues with date changes earlier, but after the recent 
commits that were supposed to fix some date-changing problems, things 
seem to have become worse. I can't track down exactly what's 
happening, so I hope it's not just ghosts haunting my server after 
midnight. :) Things I see include the sort order being reset to 
arrival, mailboxes not being updated when changing to them and mails 
have arrived since the last visit, messages not being expunged after 
deleting by moving to trash.