Usually bringing a girl back to your place before any serious escalation is best practice. (Anything more than making out, or underneath clothing). Unfortunately, sometimes the situation does not permit for bring the girl back to your place, or the heat of the moment gets in the way.

Anyways, sometimes I cross the threshold from making out to foreplay at either the girl's place, a friend's place (her friend/ or my friend), an isolated location at a party, etc. The problem is that although other people are not in the same vicinity, they are still close enough to prevent further escalation, or prevent you from bringing the girl home. So basically at some point I get cock-blocked, which does not look good for the girl or me.

My issue is that when I see some of these girls again I am not able to continue where I left off sexually/during the escalation.

I suppose the problem is can be a combination of things:
1. Backwards rationalization on the girls part. She thinks that since we did not hookup the first time and looked bad getting caught in the process of the act, then there must be a reason why we should not hookup at all. Perhaps getting cock-blocked and prevented from succeeding the first time lowers my value in her eyes, or she does not want to feel like a slut.
2. Maybe I am not being as alpha and ballsy as I was during the original hookup attempt in a semi/private/public place. I suppose I expect that we will continue where we left off during the escalation, so the overwhelming desire to make a bold move in the moment does not appeal to me.
3. Perhaps the girl does not feel that I desire as much as I did during the original attempt. She may think that since I got cock-blocked, and put in an awkward situation the first time, I do not care enough to trying again.

Any help is much appreciated.

I think the whole situation becomes associated with negative feelings when you get busted. A negative anchor is created in the girl's mind associated with making out with you. Her backwards rationalization tells her that "it was nothing more than a flirt anyway", and there may be some truth to that, depending on your game.

Depending on how superficial your relationship with the girl is, you could probably benefit by trying to bond with her a bit more, trying to connect with her at a deeper level and get to know her. That will make it "more than a flirt" so to speak, and you can always get back to her the day after and say "I'm sorry about yesterday, it was embarrassing... But it was still fun", confirming her feelings to build rapport again, and take it from there.

If you want to avoid these situations altogether, I would recommend that you interrupt the makeout before it goes too far. Tell her that "we need to take it easy", feeding the fire in her even more, and plant the idea of having sex with you in her mind - making her think and dream about it.

I can see how the negative anchor is likely the case. For what it's worth, a lot of these girls want to be friends with me after the failed attempt. I am not sure it that is their way of slowing things down, or a way to reconcile their ego in the sense that some guy made them look bad/easy and instead of vanishing the girl keeps the guys around as a friend to win back some self-repsect...IDK