Hi, I'll take a stab at this, since you helped fill in some of the blanks...
1) I would find a weekly time that (by mutual agreement) would be most acceptible for a re-boot. In my case, we currently run two shifts locally, but no weekends, so I could chose before 6:00AM, after 9:00PM, or on Saturday or Sunday to re-boot. I have made the general statement about the times selected; that the system "may" be unavailable for maintenance during those times. I've yet to have a complaint.
2) Since you are having some "system resource" problems, I would lobby strongly for idle time-out rules. I don't know what your backend systems are, but maybe something could be done there. I understand how 30 minute inactive logouts might be a nuisance, but how about 4 or 6 hours inactive? You may still be tying up resources and that could be part of your troubles.
I hope this helps,
---Will