IRS BETA Repair

Have you tried without the amp turned on plug one side at a time ( servo cable from speaker) and see which side shuts down the servo control. I suspect it is a cable problem. If you need service on your servo unit Bill Thalman at music Technology serviced one of mine and did a great job on it. ( no affiliation)

Where are you located?
I may have someone who can help.

I am using a pair of Infinity IRS Beta speakers also and love them.  I have heard that people in Infinity consider them sounding even better than their IRS V.  
I suspect it is the plug of the small cable from the control box to the base speaker that causes the problem.  Perhaps you can unplug the cable, open up the 5 pins connector and see if there is a short circuit anywhere or a broken connection.  Beyond this, I have no idea what the problem is.  
May be one of the surrounds of the speaker units is broken and requires replacement as if the speaker cone is touching the unit and unable to move, the servo linking all the driver units will step in to try to make the broken unit to move like the rest and cause the amp to trip.  
Good luck.  
I think what rvito suggested in using Bill Thalman at Music Technology is a good one and may the right one to follow.  

c421c.: Great to know you are another IRS Beta owner.  Where are you in the US?  If we are near to each other, I really like to get together some time to share our experiences.  I think my pair of IRS Beta is working as well as they could but like to listen to other people's Beta to confirm I am not too far off.

Also, the Infinity Loudspeaker forum over at Audiokarma.org is a good resource. Lots of vintage Infinity users there who can likely assist.