Heater elements not lasting long

I have replaced my heater element twice and after one use it just stops working. I think I figured it out but could use some reassurance:

The heater pump must be going out because sometimes the flow is extremely low. If the element gets too hot does it blow a thermal fuse or something?

If I fix the pump should a new element be OK this time?

Thanks for your thoughts.

Yes you are on the right track. If that pump is not pushing enough water through the heater the system will not send power to your heater. It is for safety reason, so your heater will not burn up.