Check though all the fuses. If that's not it you probably have a loose connection or corroded wire. Corrosion is common if you've been through a lot of mud and water. And yes it can be quite hard to find that bad wire.
I have had this issue numerous time on different times different machines, 9 chances out of 10 it is you CDI box...
burn it
check the pick up coil on the left side cover of the engine they have a stator and a little box that's the pickup coil check if its damage or the ignition coil
Ignition Coil braking down?
follow spark plug wires back to other end & that is your coil
check the coil
Check coil! Check coil!
there are four spark plug wires that run to the distributor..the fifth one is the coil wire
Either the coil is bad or the ignition control module is bad.I would think the coil is faulty.
Coil, distributor, bad wire.
check points could be coil or stator
soundlike you are haveing a eltrical problem ether the coil statior or may even be possible to have sheared the woodriff key on flywheel there are ways to test your coil and statior
An 88 Honda trx 350 should have a set of points and a condenser under a side cover on the engine. If the points do not work properly of the condenser is bad then there will be no power going into the coil and there wont be a spark.