I'm from India, living in the UAE. I'm going on vacation and returning to the UAE one day before my visa expires. Will I have a problem re-entering? I've heard that you have to re-enter at least one week before the visa expires.
You don't indicate what type of visa you have but, as you say that you live in UAE, and that can't be done on a visitor visa, and are Indian, most likely you have an employment permit which allowed entry, followed by a resident permit.
Despite news articles which suggest that visa renewal can be done while in UAE, other reports are contradictory.
During live chat with Ministry of the Interior agent Maha, and consistent with @pnuts feedback, you must contact Immigration before attempting to re-enter UAE:
Tel: +971 4 313 9999
Tel: +971 8 005 111