ACR X HAD LTSS FROM ACR Y DUE TO ACFT EQUIP PROBLEM STUCK MIKE.

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I WAS WORKING A HIGH ALT SECTOR N OF ABQ; NM; WE WERE HOLDING 5 ACFT BOUND FOR LAX DUE TO EQUIP OUTAGES AT LAX. METERING TOLD US TO SEND THE HOLDING ACFT ON THEIR WAY. ACR X; FIRST IN HOLDING WAS CLRED R TURN DIRECT GUP IN COURSE; AT THIS TIME; WE ACCEPTED A HDOF ON AN ACR Y 30 SW OF CIM SWBOUND. BOTH ACFT WERE AT FL350. AT THIS TIME WE EXPERIENCED A STUCK MIKE ON FREQ. NUMEROUS ATTEMPTS WERE MADE TO CONTACT EITHER ACR X AND ACR Y THROUGH FSS; OTHER ACFT; VHF GUARD; ARINC; AND VOICE WITH NO LUCK. FINALLY; ABQ FSS CALLED SECTOR 16 LOW ALT SECTOR AND ADVISED THEM THAT THEY WERE TALKING TO ACR X. AT THAT TIME; FSS WAS INSTRUCTED TO TURN ACR X 30 DEG TO THE R. WHILE STUCK MIKES ARE NOT VERY COMMON; I FOUND IT HARD TO BELIEVE THAT NOT A SINGLE ACFT OF WHICH I WAS WORKING APPROX 15; RETURNED TO THEIR PREVIOUS FREQ TO ADVISE THEM THAT EITHER WE HAD A STUCK MIKE OR JUST TO BE GIVEN A FREQ TO WHICH A CTLR COULD MONITOR THEM. I DO NOT KNOW ALL THE PROCS THAT A PLT USES IN THE EVENT OF A STUCK MIKE; BUT I FEEL THAT IF THEY WOULD HAVE RETURNED TO THEIR PREVIOUS FREQ OR MONITOR VHF GUARD; AT LEAST THEY WOULD HAVE BEEN TALKING TO A CTLR AT WHICH I COULD HAVE TOLD THEM TO GIVE CTL INSTRUCTIONS TO THOSE ACFT THAT I COULD NOT TALK TO.