Alkaline batteries when fresh are 1.5 volt. NiMH are 1.2 volts. So you get 12 volts for 8 alkaline, 9.6 volts for 8 NiMH. Alkaline batteries tend to drop their voltage steadily as they discharge, while NiMH tend to stay near the 1.2 volts and then drop quickly when they run out of juice. Most electronic devices have an internal voltage regulator that limits the voltage to the circuitry, so even if you pumped in more volts it would not matter, as some have suggested trying in these forums over the years.
Best thing to do is get another spare alkaline pack, or use the one that came with the detector and fill it with NiMHs. I've tried several kinds over the years and right now am using eneloops. They are low self discharge batteries, which means they hold a charge much longer than standard rechargeable, but typically have a lesser Amp hour rating. Makes a big difference if you don't detect and/or recharge often. You could tear apart the factory rechargeable pack and replace the batteries, mine is also to the point were it won't hold much of a charge. But it is glued together and might be hard to reassemble. I think I picked up a couple of spare alkaline holders a few years back for not much. NiMH batteries are a couple bucks apiece. I have both a MAHA charger that will charge the whole pack, and a Lacrosse charger that you have to charge each battery individually.
Chris