Slow access to network location

Question

I am using sqlite as the database in my application.  There are up to 4 computer accessing the same database.  One computer holds the database, the other computers access the database using a network path string.  The application has really slowed down recently, but if I test one of their databases using my computer ( with no network access ), it runs fine.   I am trying to compare the systems to find the issue. Does any of this sound like a possible culprit for the slowdown: ?
avast antivirus on three-four computers slowing down queries?
dual core processing behaving strangely?
Their programs run for 12+ hours on end, and their systems are rarely restarted.  Maybe something isn't dumping right?