Why does my hoverpad flip over?

Solution 1:

You've managed to stumble upon the pendulum rocket fallacy. Don't worry, you're in good company; Robert Goddard, the inventor of the liquid-fueled rocket, famously made the same mistake.

Here's a nice video by Scott Manley demonstrating the issue:

Scott's video also suggests one potential solution; if you can mount your engines on flexible supports, in such a way that they'll tend to preferentially flex towards the ground, you may be able to get your vehicle to stay upright. It may be somewhat difficult to plan a configuration that will work, though.

Alternatively, just turn on the SAS and make sure your vehicle has some control mechanism (gimbaled engines, RCS thrusters or reaction wheels; you probably don't want aerodynamic surfaces if you're trying to hover) for it to steer with. Note that older KSP versions had a bug where gimbaled engines mounted above the center of mass would steer the wrong way. That should be fixed in KSP 1.0, however.