Sleeping queries blocking rebuild index and update statistics job in Always on

At one of your client sides we have configured Always on with synchronous mode.Also we have schedule rebuild index and update statistics job which runs in night every alternate day. the issue is there are more then 100 sleeping queries which is blocking update statistics job.

I have to stop update statistics job manually once i come to office.

once i have even killed blocking sleeping query but then other sleeping query blocked it and so on.

what is the issue and please suggest some solutions

Regards Anoop