I agree with the above poster, it is now time to upgrade to vBulletin.
phpBB is good for small boards but when you get about 100 folks online at the same time these problems crop up.
I run a very large vBulletin forum (with 80,000 members and almost 1 million posts) at
http://www.satelliteguys.us it started with phpBB but when I grew to the point when I had over 100 online I had the same problems and needed to upgrade. (Now I have around 2,500 online at the same time for most of the day)
I am sure many of us could all kick in $10 or $20 each and within a day you would have the $170 needed to buy vBulletin.
Vbulletin can import all the users and messages fromo phpBB and you would see a great performace increase, plus in addition there are a lot of easy to install vBulletin add ons you can download from vbulletin.org which can give you a bunch of new features.
Best,
Scott