Yes, you absolutely should be. Your air conditioner runs in cycles, not continuously. That means that once the desired temperature is met the system will shut down, and will resume operation when the temperature dips below the target once more. However, the AC should not be cycling on an off very rapidly, especially if it is shutting down before the desired temperature is achieved.
This is called short-cycling, and it is a very real problem. As is so often the case with air conditioning system problems, there are a few different potential causes of the issue. Hiring a trained professional is the only way in which to determine with certainty why your air conditioner is shutting down prematurely.