Can an EPROM be "refreshed" without UV erasing?
When the EPROM is erased, all the bits are typically read as ‘1’, so each byte is 0xFF.

That is the way they will tend to age, with time and high temperature or radiation.

If you don’t have access to a suitable high intensity short-wavelength UV lamp to erase the chip you may able to refresh the EPROM, there is nothing in the EPROM itself preventing it. A given programmer may or may not permit this- for example the OTP micro controller programmer we use for NXP parts performs a non-optional blank check before programming, so it’s not possible to (say) add serialization to a blank area of the memory of a device that has already been programmed. 

Of course this only applies if you are programming the exact same pattern into the EPROM. Even if the data is equivalent but not exactly the same, the attempt will almost surely fail. 

Germicidal lamps can be found in water treatment units but take care of exposure to the light which can cause skin burns including corneas. EPROM erasers, usually equipped with proper interlocks and timers, are cheaply available on eBay etc. You could also try leaving it out in direct sunlight (no glass or plastic over top of the quartz window) for a few days. I'm told that will will work, never tried it. It would be better to monitor the EPROM for erasure and then expose it for several times longer than required to read all 0xFF to ensure full erasure, otherwise those '0' bits could come back under different conditions of voltage or temperature.