First is location. Do you have it where it is getting hit with air from a vent, maybe in direct sunlight (I doubt this one with your specific problem), or is it where opening an outside door can change the temperature? It needs to be where the room temperature is stable.
What is the room temperature? The recommendations are that it be in room at least 70* Fahrenheit. I've used my Hovabaor 1588 in a room that the temperature was in the mid-60's and it worked, but maybe I was lucky.
Is the lid on tight? Along those lines, is it plugged in? Have you tripped a circuit breaker where it is not getting power? My wife used to work on computers at a school. The first steps if a computer was not working was to see if it was plugged in, getting power, and turned on. Checking out basic things saved her a lot of aggravation. You did not mention how long it has been at 96. Is it still dropping or has it stabilized there?
I hate those dip switches on mine. They are a pain to work with. Have you tried toggling the dip switches. If it is like mine, number 4 should be on and the rest off. It's possible in taking the lid off and on, that dip switch got jarred out of position. I know it should not happen, but.......
Did you just put cold water in there? It takes a while to warm back up. Air temperature should warm back up a lot faster than water temperature, so I doubt that is it, but maybe give it a bit of time?
Have you had to use those dip switches to reset the temperature? When I have a short power failure, mine seems to go back to factory default, which is about a half degree too high.
Now a basic question, Have you calibrated your thermometer and how much do you trust your thermometer? Certainly do not trust the thermometer that came with it. You need a good one. I think a whole lot of temperature problems with incubators are thermometer problems much more than thermostat or incubator problems.
Just a few thoughts off the top of my head to get the conversation started. I don't mean to insult your intelligence with some of them, but sometimes the basic things are right in front of you. I like simple solutions.