"个人问题" generally can refer to one of two things:
1. personal/private reasons (as you pointed out)
2. due to fault of my own, my own incapability
"个人问题" is just a general expression to indicate that the problem is on your side/end. In a relationship, it may imply a lot of things... But ultimately, you're saying the problem lies with you.
If we wish to be more specific, we could say 私人缘故/原因 to indicate that an issue is of private/personal matter.