IRS BETA Repair

Michael Marks may be able to assist you. You can look him up on eBay where he goes by the user name magicmarksy. He is an expert on vintage Infinity speakers. I think he offers repair service for the servo controllers and he may have a unit for sale if needed.

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PS Audio is a audio manufacturer in Boulder CO.  You can go to their website and ask Paul if he can give you some advise or recommend those who work on these speakers. Possibly as reubent suggest Michael Marks is the person. I suspect Paul knows your speakers well as he and Arnie Nudell were very close friends and business partners. Arnie Nudell was one of the founding fathers of Infinity. I’m sure Paul will be very helpful or lead you in the right direction.

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.