Alt-O > Display I think. I don't have mIRC here to check. Just check one of the last sections in the options for buffer. Like I said, though... that probably won't be the issue if it's locking up completely rather than just freezing. argv0's comment about drivers is more likely the issue. There are times when having the newest driver is worse and vice versa.
Btw, your internet connection has nothing to do with slow downs caused by buffer or logging. Those are internal to your computer relating to RAM, hard drive, and CPU.
I still think it would help you to find out if it freezes at regular intervals or if it's random. You could time it with a watch or else run a timer script that displays every second so that you know when it stops by looking at the number of seconds. A good test would be this:
on *:start: { .timer 0 1 echo -s $!time(hh:nn:ss) }
Then, exit mIRC and start it up and leave the status window in focus. Take note of the time it starts (including seconds). It will keep showing the time every second. Leave it until it freezes and then note that time. Once it freezes, close mIRC and repeat. Do this at least a 3-4 times. Then compare the times and see if either: 1) it freezes at a specific time (such as right at XX:50:00 or whatever), or 2) if the time between when it started and the time when it locked up is the same each time.
Note that if mIRC doesn't lock up permanently, but only freezes for a short time, you should not close mIRC, but let it unfreeze on its own. Otherwise, you can close it each time you test.
If there is any common thing in your results (such as the 2 results I mentioned), post the results here. Commonality in the results will tell us that something timed is happening and will narrow down the possible causes. If it's completely random (for both results I mentioned... not just one of them), then it also helps narrow the cause down, though not as much.
Beyond that, you might also try an older version of mIRC and see if you have the same problem.