I have had an RO unit for many years. Once in a while the drain stops working and my maintenance man said to back flush the little fitting on the drain line. Is that merely a check valve? If not, what is it? Is so, how does back flushing a check valve have any effect? Shouldn't it just not flush backward?
Most likely you have a plugged flow restrictor. The flow restrictor regulates the flow of waste water away from the membrane. If it is plugged for very long, the membrane can become fouled so you might need to replace the membrane and also clean/replace the flow restrictor to restore production.
From the Watts Premier WP-4v manual:
The procedure might be somewhat different if you have a slightly different model.
Regarding the handyman, I have no idea what he thought could be back flushed.