Try to run it with some logging options and then paste content of file here.
Ok, it was a bit difficult getting log file as the default antminer S1 settings hides cgminers display. So had to kill process and run my own cgminer outputting to log file.
Ran it for 5 mins.
.
.
.
This is using the binaries from here:
https://github.com/kanoi/cgminer-binaries/tree/master/AntS1Nicehash website says ~60% reject rate.
The only thing that comes to my mind is that this miner is modifying ntime. We don't allow modified ntimes, because we have no methods to evaluate whether modified ntime would be accepted by remote pool or not. There should be a way to force miner not to modify ntime; in fact, there is plenty of extranonce2 size so the ntime doesn't have to be modified. Guess that is the change compared to older miner.
ntime is modifed. As is valid on all good pools.