Perhaps you spoke to them 1:1 for just that bit too long. Lots of people like to mingle, and if you sit talking to just one person in a larger social setting, it can really cut you off from the rest of the group. So in that respect it is quite antisocial to expect someone to talk only to you at length, and people will get fidgety.
However, it is a bit thoughtless and socially inept if a group of people leave one person sitting by herself, by the sound of it looking obviously uncomfortable - we've all been there and it's not pleasant. Some people are more comfortable mingling than others, but will try to include others if they look isolated. Others prefer to join their comfortable clique.
Personally if I wanted to move on to talk to someone else, yes I would get up to get a drink, but would've asked if you wanted to come for one too, then go over to a group and introduce you to others / let you mingle there, rather than walking off and leaving you alone. Not everyone has the same social confidence.
Rather than worrying about the person who has left and why, did you look around for someone new to talk to, anyone else by themselves? It is harder if everyone is sitting down, but if you find yourself isolated, generally better to get up and change where you sit / stand, move around a bit. to mingle better, even just go to the counter for coffee. So, put the onus on yourself to mingle, not on others to stay with you because you strike up a conversation.
As for the playdates, I wouldn't worry too much about not knowing the other Mums well, it's about your child and who they would like a playdate with, not whether you and the Mum will be friends. I have in the long -term met some lovely friends through school, but it takes time, and for the majority it's just about the children, and they will chop and change friends through the school years anyway. Just ask them, that's how you make social connections for your child.