Bike was working fine, then wouldn't start. Battery is strong but starter relay clicks and power comes on enough for lights to come on but when I crank it, the bike clicks at the relay and shuts down. Then resets (sometimes) and then the whole thing goes on again.

What do the lights do when you try to start it? A battery can be strong enough to power lights, etc, but still not have enough power to handle a big draw like the starter motor.
You could also check cables going from battery to starter relay and relay to starter.

From your description, it sounds like a bad starter motor. That is provided all of the cables going from battery to relay, and relay to starter are not corroded or have poor connections. The relay is a weak point, so it may be damaged as well if the starter has been pulling too many amps.

you may have blown the starter solenoid or even worst the starter motor
i cannot diagnose without seeing the bike properly
i strongly suggest you put in a workshop and get it diagnosed properly

Check to make sure you are getting 12v to the starter when you hit the start button. If you are,then yes,...most likely the starter is toast. But if youre not,..then check all fuses and the starter relay.

Look at the end of your starter. There's a five-sided plate on the end held on with three small screws. Just above it, there is a single wire plugged onto the starter. Pull this wire off and connect either a test light or a volt meter to the wire. Turn the switch on and press the start button. You should see the light light up or the meter should show battery voltage. If you show voltage at this wire but the starter doesn't run, the problem is in the starter. If no voltage at the wire, your starter relay may be bad. I think the starter relay for your bike is behind the triangular plate on the left side of your bike. The relay is a one inch plastic cube just like the relays on most automobiles. With the switch still on, press the start button. You should feel the relay "click". If it does click, you might want to replace the relay and retest the starter wire. If it does not click, it could still be the relay or it could be the wiring between the start button and the starter relay. Since I don't have a wiring diagram for your bike, you may need to purchase a service manual to obtain one or find it from another source. I wouldn't think the installation of a muffler would have anything to do with the starter operation.

Good Luck
Steve

If you hear the starter relay click, but not turn over the motor that's a classic low/dead battery situation. There is only enough power left for the battery to click the starter but is not powerful enough to actually turn the engine over.

three ways you can deal with this issue.
First replace the battery.
Second give the battery a charge using either a battery charger or the more common battery trickle charger (battery tenderizer) which most motorcycle owners use to keep their bikes battery charged over long periods of non use like the winter. If you have a tenderizer just hook it up to the battery, plug it into the wall and let it trickle charge for about 12-16 hours or so and then try again.

If the starter is actually turning over but you arent gettting the engine to fire then it has to be one of the only two remaining variables that we need for combustion, spark and fuel. check you spark plugs for excessive wear, carbon buildup or damage, and then check the spacing or just replace them. if you see a spark when you fire the starter than its not a plug issue.

Finally fuel. Is there gas in the tank? can you hear the fuel pump click on once you turn the key to on? is the line creased or corroded, if you unplug the line do you see fuel being pumped in?

those are your three possibilities.

Another easy thing to try to check if it is a batteyr issue and you don't have a charger is to try push starting the bike

1. First, make sure that your bike isn't starting just because you are out of gas. If you're out of gas, this will not work.
   
2. Make sure the key is in the on position
3. Put the bike in 2nd gear
4. Hold the clutch in and begin pushing, preferably downhill, but it will work elsewhere as well.
5. Once you've gathered enough momentum, apply a minimal amount of throttle (not too much or the bike will get away from you) and hop on the bike just as you release the clutch.
6. Rev the engine a bit so your bike doesn't conk out.
7. Ride away.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_cd01d4e4178e5a11

have you checked the kill switch. It can be easy to knock this accidentally.

Clicking points to either bad battery connections (corroded) or a low battery (does not take half as much power to work hor or lights as it does to turn the starter. Also check starter relay and neutral safety switch.connections.

start relay should be checked, if cables are loose or corroded they do not deliver enough power.if jumping the start relay will engage the starter replace the relay.

Have you tried charging the battery or jumpstarting it with another battery?