tweeter cutting out, what to do

I have a pair of Infinity Kappa 8.1 vII's powered off of a Adcom GFA-5500 & my receiver is a Denon AVR-3000 (yea, as old as the speakers, early 90's).

When I play a CD at close to half volume the tweeter on my right likes to turn off for a while. Any thoughts on what I should do to correct this? I do not want to damage them....

Should I buy a new receiver/processor or would a larger amp fix this?

This sounds as if the problem is with the speaker if it's only the tweeter that cuts out. Are the speaker biwired? If so, check the speaker connection for the tweeter. Also, try swapping the speaker leads left to right at the amp to determine if the problem stays with the speaker. It sounds more like a connection issue with the speakers or maybe a heat issue with the tweeter or crossover.
thanks for your help

I forgot to mention I can play music from XM/DirecTV at over 3/4 volume with zero issues.

The speakers are not bi-wired & I will swap the leads now
Oops... I meant to say they are bi-wired

I did swap the leads & it's still cutting out the same tweeter. Could it be the wiring inside the speaker or the tweeter itself?

Yep. Could be either. I'm not familiar with that speaker but I'd check the internal wiring if possible to get in there. Looking for a loose connection or cold solder joint. Good luck.
switch your speake wires, right to left and left to right, and see if the problem moves. If it moves, the problem is not the speakers.

Also check your interconnects between the CDP and receiver. I was demoing a new CDP, and the one interconnect was not tight, so my one speaker cut in an out until I tightened the connectors.
If I remember correctly, quite a few Infinitys have self-resetting tweeters. I know my Rennaisance 90's (aledgedly) do according to the manual. Although I have never heard mine go off then re-set, I have heard my friends Kappa 7's do it. I believe your Kappa 8's may be doing just that. If that is the case your amp may be clipping and causing the tweets to cut out. My friend increased the size of his speaker cable and mentioned that he is now able to crank it up quite a bit more before the problem happens again. No fancy cable stuff, just a larger Monster gage. It looks to me to be around 10 gage. This may be a cheap fix for you and make the system sound & work better as well. Perhaps try the wire & check all connections if you want. Hope it works out for ya.
Good luck, John