If you make something happen (or something is made to happen) there is an actor who is the cause of the result. In contrast, when you have something happen, there is no actor, or the actor is unimportant. It simply happens, without cause.
Compare these two sentences:
The other night, my girlfriend made us a nice dinner.
The other night, I had a nice dinner with my girlfriend.
In the first sentence it's clear who made the dinner. In the second it's not, possibly because I don't think it's important.
In a similar way when talking about an old ailment, having the symptoms return implies there is no significant reason for it (unless you provide additional information). It just happens without cause.
The changing weather is making my old knee injury flare up (be in pain).
I'm having pain from my old knee injury.