Discounting brings its problems, as when you discount for someone, it is always hard to increase back to normal rates. We never discount, but do run lower prices occassionally on-line. Only you can decide if your margin is open to discounting.
As feedback from ITSALIFE, make sure that if you are discounting that it is dependant on guest staying the length agreed, as many will look for a weekly rate and check out after a few days.

We shun long term stays and do not take bookings over 4 days. This is largely due to our rooms not containing cooking facilities and guests that start off fine and finish off treating the place as if it is theirs and slowly creeping in their own cooking facilities, etc.

However, I am sure that there is a lot to be said about longer term, but beware and ensure that the guest is always paid up in advance and the minute you start getting excuses of late payment, let the alarm bells ring and get rid of them.
Too often, we hear of motels being owed hundreds or even thousands of dollars that they will never see.
I personally would not issue an account to anyone that is not a government department, and would always insist on a purchase order outlining dates, tariffs, etc.