ZAB Controller reported frequent radio equipment failures with limited coverage and failure of MSAW feature resulted in an aircraft entering a higher MVA at too low of an altitude.

Narrative

Aircraft X; entered a portion of an MIA (Minimum IFR Altitude) box of 7700 ft. while at an altitude of 7000 ft. The aircraft was being vectored by the R-side to be cleared for an approach into P08. While on this vector; a sector with moderate level traffic lost its frequencies; making any sort of air traffic extremely difficult. As the D-side; I was offline coordinating with surrounding sectors and facilities to get aircraft placed on a backup frequency. In addition to the frequency complication; at no time did an MSAW (Minimum Safe Altitude Warning) alert start flashing on the scope. Typically; this alert will flash minutes in advance giving plenty of time to correct the issue. In the Southwest area of ZAB; we have issues with our frequencies relatively often. Sector 42 has lost frequencies on multiple occasions. Other sectors have dead spots of radio coverage. For this to happen on a small busy Sector such as 46; it can be very dangerous. Also; the matter of the MSAW alert not flashing should be addressed. Had this safety feature worked as intended; I would not be here filing this report.