Have you had your roof inspected by a roofer? I don't mean some guy at an RV dealership that occasionally replaces a rubber roof. I mean a guy who is licensed to install and repair EPDM roofs.
As a contractor we restored a lot of EPDM roofs. If the substrate underneath is in good condition, there is usually no reason to replace the entire roof. Places that fail are usually the seams(not present on RV applications), flashing and penetrations. These areas can be cleaned and renewed with new material to extend the life of most EPDM roofs to well over 20 years. The cost to renew an EPDM roof is usually about 30% of a complete roof replacement.
Of course if you have an area of rotted wood, which is usually at a flashing or penetration, it is repaired when the old flashing is cut back.
EPDM roofs have been used for decades on commercial buildings and on some residential applications. The last project that I did with an EPDM roof was 80,000 sq. ft.
It might be prudent to have your roof inspected by a licensed roofer rather than some employee at an RV dealership. You may find that all you need is some basic reflashing of certain areas and that the main portion of your roof is good for another decade.