Originally Posted by blackberry1
Look for Memory Leaks in the Event and BES Debug logs on the Windows server hostng BES
Does reboting the BES fix the issue for few days?
Good one. Didn't even think of that.
And blackberry1 is 100% right about MSDE. You can only have 8 concurrent connections to it. There is a concurrent connection checker on the MS website that can help you check for that.
But the more info you can give on the environment, the more people can assist you with possible solutions.