Controlled computer becomes unresponsive, have to reconnect and keep trying

Question

This has been happening for a while, back when I had 10.5.6 and now when I have 10.5.7 (combo). Sometimes when I connect to a computer remotely, by using ARD, as soon as I connect nothing reacts in the computer that I connect to. So lets say I click, move stuff or anything like that, what I see in the screen is completely static.
But, if I close the managed computer's window and reopen again, whatever I did shows up, but whatever I try doing again doesn't show up (it's still unresponsive).
To fix this I have to restart the computer, and it works as it should.
How can I get rid of the problem?

Answer 1

I was able to find the definitive solution for this.  I noticed that my computer was freezing approximately hourly and began to suspect my Time Machine backup solution.  After a few more steps of ruling out one variable after another I learned that Sophos (free) anti-virus was, indeed, interacting with Time Machine and causing the problem
Sophos uses a technique called "Scan on Access" which means that no files are scanned for viruses (after the initial scan) unless they are accessed.  The problem is, when you perform a Time Machine backup many files are accessed and the machine slows to a crawl and then becomes unresponsive before you can detect it using Activity Monitor.
I like Sophos, in concept, and disabling Scan on Access solved the problem.  But, then I did not have a live anti-virus/malware detector which, regretably, is becoming more important for Macs these days.
I uninstalled Sophos and my problem is resolved.  I installed another well-known reputable anti-virus tool (that uses a different strategy than Scan on Access), and the problem did not return.
I hope this helps.
Best regards,
John in Fort Collins