It really just depends on why the server is giving you the cold shoulder. I went with the most obvious; number of simultaneous connections. If that's the case, dropping to 1 (i.e., not parallel at all) would resolve it. But it may do rate-limiting, shoving you away after a given number of responses in a particular time period. It may be server load dependent. It may just be flat-out random.

Likely, the only way you can find out for sure what's up is by talking to the server admin. The best solution code-wise is to be adaptive; if you start getting errors, slow down, if you get no errors for a while, speed up. But that's a lot of work to get right.