Yahoo !! One year has passed since I got on different projects the 'General Network Error'.
Check with Google and you will see a lot of people having the same problem. It's a shame but this error doesn't throw a managed exception so the try catch sequence dowsn't works in this case and you finish with a poor user friendly .Net error page!
Thankfully I won't have to celebrate another anniversary because I finally managed a solution.
Add max pool size=7500 in my connection strings and then problem solved.
I know 7500 is a big value, but if I try a lower one, I have the error back. Now my sites are running full speed.