I'm having a very similar problem and it began about a week ago. I've had these forums for years without any issue, on the same host (JaguarPC). I'm on SMF 1.1.19.
It only seems to be effecting Private Messages. Posting to the forums itself doesn't seem to be a problem. If they are using IE, they get the following error message:
Database Error: MySQL server has gone away
File:/home/blablabla/public_html/Sources/Subs.php
Line:631
In Chrome, it just sits there 'waiting'
I didn't make any changes to the forum. I did do the recent security update, but the problem was there before and after. Jaguar did increase the timeout settings for me, but it hasn't made a difference. So far, it's occurring mostly with PM responses, but I had it happen to me in Google Chrome for the first time when trying to send to 2 recipients.
Also, nothing in the error logs and I have no mods or customizations.
It seems to fail on a query updating the members table.
Could you check if SMF is configured to use persitant connections ? If so uncheck checkbox.
I can confirm in my case that the box is not checked.
Hylander, in your case, it sounds like a problem with the database server. That error message is a very common issue on overloaded database servers where the host has configured very short timeouts.
As for mark48's issue, it seems really tricky, but may be related to something specific to the new environment in which the site was placed. I'd suggest looking over and disabling or removing any modifications that are non-essential to get as close to a vanilla SMF system as possible and see if the issues continue.
Unfortunately they have already upped the timeout time for me, and that has not solved the problem. Everything else on my other sites seem to be working perfectly fine. In fact, everything else on the forum is working perfectly fine except for private messages. Logging in, posting, etc is no problem at all.
I've split this off, from the original topic, for obvious reasons.
Hope nobody minds. :)