James brings up a good point with the rubbing alcohol - some people simply have more "reactive" sweat and kills string quicker (I'm the opposite - I rarely sweat through my palms and the "new string" sound lasts me months). You also might want to try using an alcohol-based hand sanitizer
before playing as well.
I can think of two options in addition to the alcohol wipedown. First would be to stay with your normal schedule of string changes but you less expensive strings/bulk-purchased set to maximize your money-to-usage ratio. A few examples would be D'addario's XL Nickel twin-packs or XL ProSteels, which are my personal favorite strings for fretless (Nickels) and fretted basses (Pro Steels) and a great bargain, or to buy store-branded or bulk strings, although these can be a bit dodgy in terms of quality.
Carvin sells rebranded strings and have gotten pretty good reviews.
The second, as mentioned previously, would be to switch to coated strings such Elixer, DR's line, or D'addario's EXP line. The negative is that none of them have the brightness of brand new strings for the simple fact that they're covered in a softer material and that they're significantly more expensive. However, I've heard good things about people with deadening issues like yourself getting great results with these, and that usable string like is dramatically increased (D'addario claims 3-4x longer life). Generally I've heard that EXPs have the closest tone to "normal" strings.
