I have a 2011 and I experienced this issue where my headlights, horn and running lights stopped working. I should state that I felt I should try to investigate this myself before paying somebody, however, I have no vehicular electrical experience of any kind. (Well, I don't have any electrical experience beyond a potato battery experiment in grade 3...)

I found one post on the site here were a guy had this issue and found a loose connector. Indeed, my issue was caused by what I believe is the same connector. However, the connector itself is not loose (as his was) as when I ziptied it together, it didn't solve the issue. Upon further experimenting, I found that moving the wires around the connector caused it to fail, but no particular movement consistently caused it to fail. I did notice that one side of the connector was getting really hot, like almost too hot to touch, the culprit seeming to be an orange wire. In the absence of a wiring diagram, I thought I'd try and isolate the offending part. As soon as I unplugged the headlight, the wire/connector stopped heating up. The headlight bulb is correct, it's not like the wrong one is in there, drawing too much power.

I then unwrapped some of the electrical tape behind the connector, to see if it was the whole wire that was heating up or just the connector. As the wire didn't get hot, I conclude that the orange wire is maybe loose in the connector.

So my question is, do I have to replace the wiring harness or do these connectors come separately? Has anybody had any issues like this? Is there something else I should be checking?

PS, I've attached photos of the offending connector.

Odds are the connector is not making good contact.
Could be mechanical, could be corrosion.
Could be both.

Corrosion: get a GOOD contact cleaner.  I recommend Deoxit D5
https://www.amazon.com/Hosa-D5S-6-DeoxIT-Contact-Cleaner/dp/B00006LVEU/ref=sr...
Follow the directions EXACTLY.  This is expensive stuff, but really good.
You really should try this before having to resort to the next thing:

Mechanical: examine how the two sides of the connectors mate, and try to bend parts of one or the other (or both) so then get a better connection.

Thank you everybody for your responses; great advice all around and it was most helpful. The end result was that although everything was in minty shape, one of the connectors had a gap and was arcing. I cleaned it all up and bent the connector so it gets a better connection and the problem has been resolved. Time to ride! Woohoo!

There's a thread around here that has a link to a site where you can get replacement connectors and tools to work with the pins in the connectors. I can't find it. Anyone know what I'm talking about?

I've heard it said that the weakest part of a motorcycle is the electrical system,and it's true.So why do we have connectors? could it possibly be for the easy of the factory in assembly? Plug and play,but in your case, it"s plug and pay! I guess it bothers me to see people pay good money to replace a failed item with one that is subject to fail again . I would cut the connector out and toss it ,solder the wires ,use shrink tube, tape and never worry again! They will be sealed from the moisture that caused your connector to fail. fuses protect your bike ,connectors do nothing but cause heartache.

I don't think replaceing  all the connectors is good ,the majors ,like rectifier,brain box, and stater should stay .But the one we're talking about  removing isn't a biggy,and the wires still color coded.