Most importantly, tripping a circuit breaker over and over again is a serious problem.
Circuit breakers do wear out when they are continuosly tripped.
However the more important thing is that two 1500 watt space heaters CANNOT EVER run on the same circuit.
The rating of the breaker is stamped into it (15 or 20 usually) this is the amperage (or current) that can safely "run" through the wires in the wall. You can calculate how much current you are "pulling".
All appliances list the current in "A" or Amps or "W" Wattage. To find the amperage if it lists wattage, divide the wattage by the voltage ( normal two prong, or two prong with ground outlet is 110V in the US, UK I know is different and many other countries) add all amps from the appliances on the one circuit breaker, this will tell you if your breaker is bad or you have too many appliances, and if the breaker is 15Amps do not run more than 12 to 13 amps on a constant basis, 15 is the max. at which the breaker "breaks".
Example 2 1500 Watt space heaters running at the same time is....1=1500/110=13.63A...
2= 27.27 A.
The breaker and household wiring will never handle this current (it's a fire hazard), also turn off only that breaker, and go to every outlet in the house an see if it is working, a small lamp or radio which you can carry in your had to the outlets not in use makes this easy, there can be an outlet anywhere in the house that runs on that line, don't forget clocks,and light bulbs, a 100W bulb= .9Amps ( point 9) many appliances pull power when not in use, TV's VCR's Stereos, and anything that uses a remote control, it all adds up. You should contact an electrician.
You may need to add an additional breaker and power wires, which will require an electrician. This is typical in older homes when people had 1 TV, 1 refridgerator, etc.
(excuse any typo's, spell check not working)