When I start the car the passanger brake light works fine. Once using the brakes a few times the icon on the dash comes on and when I check it, it is out. Once I shut off the car and restart it it works again. ANy ideas?

Check the brake fluid level in the reservoir, I have a feeling it may be low. Fill the reservoir to the MAX level or even just a tad above it, hopefully that will cure it. But low fluid level may indicate that your brakes need to be serviced as well.

Also check your rear bulbs and put a dab of dieeletric grease on bulbs before putting back in. And do not touch end of bulb with oily fingers. Also check 3rd brake light in back window.