This took me over an hour to debug, so I'd hate for anyone else to have to
repeat the work.

The ICQ server apparently has some sort of limit on how frequently you can
connect to their server. The limit is fairly high, but with all my testing
I've exceeded it on my test ICQ number.

I tried to load that test ICQ number on Mirabilis' client and it told me
that the rate was exceeded and to 'try again in a while', so it looks
like it's not permanent. The symptoms are basically that Miranda
repeatedly sticks at 'connecting' for no apparent reason, so watch it.

The following is pure speculation:

I'm guessing the limit is around 100 connects in two hours.

It seems accounts can be connected again after about half an hour, but on a
sort of 'probation' scheme. Ie, they can be connected once but then if you
disconnect you can't reconnect for another 5 minutes or so.

I have no idea how long this probation goes on for, but it's definitely less
than 24 hours and probably around 3-6 hours.