Is it normal for the sump pump to run continuously? 

Sometimes. Continuous operation can indicate problems such as a stuck switch, a malfunctioning float, or an incorrectly sized pump and should be addressed promptly to avoid burnout. However, during heavy rainfall or snowmelt season, your pump may need to run nearly continuously to keep up with the amount of water threatening to enter your basement.

Regular checks and maintenance will help determine the reason for a continuous run.