What are your daytime temps like? You have only been using a bulb for light during the day, no heat, correct? I'm just trying to understand what your setup is like. I thought you were using a bulb to heat during the day then switched to a night time bulb, also for heat, at night. If you only need to heat your enclosure at night a heat pad may work. I wouldn't put it under the tank though. Depending on your substrate it may do nothing more then be a fire hazard since anything too deep will just trap the heat under the tank. Most people who use them put them on the back or side of the tank to warm the air. The thing with heat pads is they put out very little warmth, at least in my experience with them so if you need to raise your temps more then a few degrees it probably won't work and a bulb will be a better choice. They shouldn't be able to burn your frog unless the wattage is way too high and your temperature within the tank is dangerous. Being on the outside of the tank they should never be able to touch it anyway.

Your fixture could be perfectly fine but it's just the screwing and unscrewing the bulbs that could be the problem. Also if you are using your bare hands I heard that the oils from your skin can make bulbs blow faster. Once you figure out if you want another dome, a dual fixture or a heating pad then your problems with the bulbs should go away.