depends on what the issue is.
might be a bad connection issue which may be able to be fixed by disassembling the headphnes and checking the wire connections. perhaps even running a new wire.
if its the actual drivers then its not going to be cheap as bose probably has them marked way up in price. just look at the retail price of those headphones...and you can guess what parts will cost.
can you fix it yourself? maybe if you know how to use a soldering gun, screwdriver, and have basic skills. cost would be determined by parts.
is it worthwhile? personally i'm done with bose. the price per performance ratio is just horrible. i had a $150 pair of non-cancelling headphones awhile back which died because the thin cord broke. i replaced them with a $150 pair of studio-level headphones with a cord 5x thicker and a much better quality of build. oh and they sound much better as well. audiotechnica ath-m50s in case you wanted to know.
in your case... i'd say if the driver is bad then you might not want to fix it. if the wire is lose or bad you might want to fix it. unless its under warranty dont take it to a shop as you're going to spend more than its worth.