Yes, any of the regenerative power units made for audio should do the job. They are pricey and look for one that has some sort of backup power, whether it be capacitive (short term) or battery (longer term).
Another less expensive option is getting a basic UPS supply for computer equipment. They are less expensive than the made for audio ones. Note the price goes up as the run time without a grid increases. Less money but they work even though they are not as well suited for audio work as a dedicated audio power unit. If you do get a computer based UPS, also pick up a audio grade EMI filter unit to put between the UPS and the audio equipment. That will keep any generated noise out of your system.
Your case is one of the few that desperately needs a dedicated line!
Regardless of what you do, you really need to get a qualified electrician out to your place and verify the problem is your incoming power and not something on your side of the meter. This is important. If it is on the grid side you won't have to pay to have it fixed. If it is on your side, then you really need to do something about it. Seems to me this is a fire waiting for a time to happen.
How old is your home? When was it built? Was any electrical upgrades done to it since it was first built?