Examine the main control panel to look for error messages or location readings. If you're getting a specific error message, report it to your security company for analysis and diagnosis, or look it up in your security system user manual.
Check each individual device to see if it is getting power regularly. If the whole system is losing power, it is a problem with the installation or the power supply. If it is only one device, the device can be fixed. If power loss is taking place in one area of the house or in the devices that are all on one circuit, it could be a system glitch that would need to be fixed by the monitoring company.
Replace the batteries on all of your devices. Some devices use battery only, while others have batteries as backup for the main power supply. If the batteries are in need of replacement and the main power goes out, the device won't function.
Inspect your breakers. The security system could be drawing more power than a particular circuit can provide. If a breaker is failing, the breaker itself may need replacement, or the system may need to be rewired so its power needs are split among multiple circuits.