Windows Operating Systems prior to XP are prone to occasional problems. I have used ME myself before moving to XP and I liked the OS, although many people think it had it's own set of problems.
If the problem is as you say, occasional, then it is something you may have to live with. But you can try and minimise the problem by good housekeeping, eg;
Use a recognised firewall to keep hackers at bay,
Keep the definitions of your anti-virus, anti-spyware and anti-adware programs up to date and run regular scans with the programs.
Keep your temp folders, and Temporary Internet Files folder clean and empty.
Keep your Recycle Bin empty.
Once a month, run the Scan Disk to check for errors, and then run the Disk Defragmenter afterwards. It may be advisable to run both from Safe Mode and turn off any screen saver, as they will run better without interruption.
Keep your important files, (documents, photos, music, email settings, etc), backed up.
Keep the computer free of dust, and open the case to check for dust inside. Blow it away from the circuits using an air spray.
Check all connections.
These are general housekeeping that help to keep a computer running smoothly.
I hope this helps.
My computer occasionally locks up while I am browsing web pages. When this happens all I can do is power down and restart. The system will not respond at all.....including the mouse.
My operating system is Windows ME.