I don't think their relationship was particularly romantic. I think we viewers were increasingly SOLD their relationship as sexual, in order to titillate, around S8-S9. There was a point where Stabler left his wife and started sleeping around, and the romance between the two of them became almost canon..then he left.

Can't remember looking back if he actually cheated, or if they separated and then he hooked up with that younger rookie cop he was supposed to be training, which is also kind of gross seen through a #metoo lens.