Q: My car is experiencing braking problems.

I've had my Dodge Neon for about three years now, and it has always made a strange sizzling sound like water hitting something hot when it rains. The sound comes from the front passenger side, and happens when I turn the wheel after starting it up in rainy weather. I took it to a mechanic to figure out what was going on, but they couldn't reproduce it, and couldn't find anything obviously wrong.

For the last six months or so, I have noticed this random thing happening where I will brake slightly, and the car makes a shuddering "thump-thump-thump" and then that's it. I can't make it happen, and I haven't noticed any correlation in events, like with the rain.

Then yesterday, I put my car into reverse to back out of a parking spot on a very wet, rainy day, and my brakes seemed to fail momentarily. Scared I was going to back into someone, I kept pushing the brakes down, and finally, just in the nick of time, they worked. Now, they're fine. What the heck is wrong with my car??!

My car has 72000 miles.
My car has an automatic transmission.