Always Seeing My Ex's Birthday Numbers on the Clock

Yes, there is a reason. Or it wouldn't happen.

Generally, however, it isn't an esoteric special reason applying only to you, but a reason related to attention that's shared by most humans.

Although you look at the clock at various times during the course of a day (I assume), it is these particular numbers that you remember seeing. Generally, a person remembers seeing certain numbers because there is personal meaning or emotional significance related to the number. The number is seen, the meaning or significance is noted, and seeing the number is remembered.

Although it's been 5 years since you've broken up, and there may be no personal emotional attachment left, the fact that you wonder why you're seeing the numbers creates an emotional significance related to the numbers. That significance ensures you keep remembering it when you see the numbers. Why People See Certain Numbers All the Time describes how that is.