I have seen that every time magic gets stolen or fails, every pony panics. So why is magic so important to them?

Well, on a personal level, Magic is what lets pegasi fly, unicorns do their spell thing, and what makes earth ponies prodigiously strong and in-tune with plants and animals. It’s a fundamental part of their biology, like a sense or an appendage. Stealing magic is probably sort of like cutting off a human’s nose or ears.

I mean it varies with the kind of theft you're talking about, but at the very least magic is what allows ponies to control their world.

In School Raze it's established at least some modern convinces run on magic and the weather and sun and moon are controlled magically so without it ponies are unable to control their world, at the very least causing it to revert to a earth like state if removed entirely.

If stolen they would lose control of their world to whoever holds the magic, so they have a vested interest in keeping it safe and out of the control of their enemies.