While it's true that the request for a discount can be a red flag indicating that the guest is going to be trouble in other ways, it's not always true. In a lot of cultures, it's just normal to ask for a discount on almost everything, e.g. in India or Pakistan.
I always say no to discounts. I host mostly long-term guests and so they will frequently ask before booking could they get a discount, seeing as they are staying so long. I think that's normal. I just remind them that they are already getting a long-term discount of 15%. That is usually the end of that discussion and they book or they don't book. Can't say the ones who booked were more trouble than guests who didn't ask for a discount.
Short-term guests on the other hand... That just makes me laugh. E.g. "Seeing as we are staying three whole nights, could we have the weekly discount?" Erm, no. Same guests show up SIX HOURS before the agreed check in time with a bag full of dirty laundry that they want to wash immediately. They hadn't been travelling but flown in from their home, so no idea why they brought dirty laundry with them. Should have seen that red flag a mile off.