I suppose there are a few possible answers to this.
One thing you could check if this is a thing that usually happens in big games - do you have any players, particularly defensive ones, who dread big matches? If you have, they are probably more likely to crumble under the pressure and make mistakes.
Another probably cause is that these opponents are obviously gonna go attacking if they're down and there's little time left, and they have the quality to punish you. The quality is already one major factor that separates them from weaker opposition.
What's more, what are the things you do differently in those games than in the ones where you don't concede? (Of course, you will always concede SOME late goals over the course of the season, nothing's gonna change that)
Do you go very defensive and passive although your players aren't familiar with that approach?
I did that for some matches at the start of FM when I desperately wanted to protect the lead (like, full on, play slow, play short, waste time, don't engage, deep defensive line, cautious or very defensive even - and well, that just contradicted everything I had been training my team to do), and it always resulted in my goal getting peppered with shots.
If none of these seem like they are the answer or play a part - try to look and analyse. What do these games have in common?
How does the approach of the opponent change before they come back into the game? If you can make out a pattern, you can work to counteract it.
Also, is there any pattern in what you do? Maybe early substitutions which cause your team to be knackered while your opponent makes late substitutions and therefore has fresh offensive players?