if it's a newer honda with a capacitive discharge type coil, my guess is it went bad. I have a northstar generator with honda engine and the CD coil went bad on me within 1 hour of use brand new and the $75 replacement was bad out of the box. i converted it to the old style coil which cost $10 and has been fine since.
if you are under warranty then hopefully it costs you nothing, but it might cost a lot of time sitting at a shop waiting for warranty approval. my generator sat 2 months before i took it back and fixed myself.
changing the coil is not hard, you need a handful of metric tools and need to get flywheel cover off, but to get flywheel cover off you need to undo carburetor and handful of other things. putting a replacement coil and even a different coil in is not hard, and getting the spacing between coil and flywheel is not critical. i would look up the replacement coil online for your model/serial of engine and see if it comes up as a CD coil. if it does, you can buy a new one for around $70 and take your chances or you can consider substituting it with a traditional non-CD coil that costs less than $20 and lasts forever. and if a shop does the work and it is the coil which they replace with another CD coil, see what the warranty is on that part and labor. there is a way to check the CD coil in the newer honda engines having them, there's supposed to be an ohm reading between wires coming off the coil, if it's an open circuit it's bad. i have an older hs928ta btw.
