DLP power loss
From what I am familiar with with front projectors, losing power can cause premature BULB failure because the bulb is extremely hot and not getting appropriate cooling when the power lost.
An inexpensive UPS will prevent this, but might not have the power conditioning capabilities of a hight end model. Just match the UPS with the current draw (Wattage) of the TV and the amount of time you want it to keep running. You might be able to determine the appropriate time by turning off the power to the TV after a long viewing session and measuring how long the fan stays on.
APC, Triplite, and Belkin should all have several models available in your price range.