I would check it out, since the problem only gets worse ( more expensive ) if more of the solder joints fail.
It is a cheap fix if caught before the rest of the solder joints fail and the whole thing goes ape on you.
About a half hour with a soldering iron and magnifying glass, and you're done. If the eeprom packs up, then its about 10 dollars for a "second level" programmed chip. The problem is tho, you only get one shot with the new eeprom. It's a 8 pin chip, and it stores data for alot of things, like SMPS frequency, sweep frequency, etc, etc. When you get one, it is programmed with "average" values, enough for the set to turn on, then adjusting the TV will program the rest. There is a sequence to getting the TV to turn on with a new chip, and if you goof or there is a problem still with the TV, you just may hose the new eeprom.
All this was caused by a really poor soldering process that failed to solder the metal box and vias to the PCB.