HP 35s battery drain

[grsbanks]

I don't know what batteries you're using but cheap Chinese no-name lithium batteries are going to have much less life in them and perform nowhere near as well as batteries of a reputable brand.

This said, that the first set of batteries only lasted 3 weeks should have been a good indication that there was something wrong with the calculator. It is very likely that one of the decoupling capacitors inside it is leaking.

If your calculator is still under warranty then take it back. It is faulty. If not then you're probably better off getting another one.