Manufactures won't technically discontinue a printer ink for about 15+ years (roughly) after the printer has been discontinued. If the printer is really old and they don't see the inks getting ordered for it that often, they may start to end life of the supplies. They try to get customers into the newer models anyway. You should be good though since the 3800/3880 has only been discontinued for about 2 (3880) and 6 (3800) years, so there should be plenty of time left of ink.
Also watch how you use 3rd party ink since these aren't genuine products and "may" take a toll on the print head down the road. Some people have good luck and others don't. We never recommend using 3rd party ink in case you try to get it repaired (out of warranty with an authorized service center and they normally won't fix because it wasn't Epson ink that damaged the head). Not saying you should NEVER get them, but just keep an eye how they are used so you get the most out of your printer. The newer printers are basically getting restricted from any 3rd party ink and haven't heard anyone being able to trick the printer into reading yet.