Adding a little technoid stuff ... there are three types of devices that may be used in surge protectors. All work on the principle that if a certain voltage is exceeded, the devices clamp and absorb a lot of energy. But their diabolical details are different:
* Transient Voltage Switches are super fast, but can't absorb a lot of energy without being destroyed;
* Gas Discharge tubes can absorb a lot of energy, but aren't (comparatively) very fast;
* Metal Oxide Varistors are almost as fast as TVSs, and can absorb almost as much energy as Gas Discharge tube, and are very inexpensive.
Guess what is used in those power strips with surge protection. HOWEVER every time an MOV absorbs a transient, a little damage is done to the MOV. Not a lot, but over time and power surges, the damage is cumulative, and the effect is that the break-over voltage, the voltage at which the MOV conducts, gradually drops, until it is conducting at normal line voltage and soon self-destructs.
My guess is that either the MOVs in your power strip dumped more energy than the MOVs could handle - even if new - or that they had deteriorated to the point that a couple of significant surges fried them. So ... how is this practical? Depending on weather in your area, you need to replace your power strips with some regularity. If you live somewhere with lots of thunderstorms - like KS or NE - I'd suggest every 2 years. Somewhere like Silicon Valley, maybe every 10-15 years. Now, if you know what you are doing - I don't recommend doing this casually, if ever - you could open up old power strips and replace the MOVs with new ones of the same voltage rating and the same or higher energy rating.
FZ's thinking is basically sound. Personally, I'd plug into the UPS your computer and other devices that are both pricey and have important data, and use power strips for stuff like TVs.
ETA: I've worked in power electronics since 1980, so I have some familiarity with such things.