That doesn't work with the concept that you can take your first attack, THEN based on whether you hit or not, decide to take the rest of your attacks (for a full attack action) or move away (for a standard action and a move action).
Therefore it doesn't become a full attack action until you start swinging your sword the second time, since you could have moved away instead, and thus leaving it as a standard action instead.
Now if you want to be generous to the invisible attacker, you could say that the victim of his attack needs to succeed at a spot check, otherwise he was looking the other way when the blow landed and you can still get in a second sneak attack. But that's really just a rule0 call.
I never did like the fact that everyone on the battlefield is instantly aware of any person that has their invisiblity broken and instantly gets their full dex mod versus them. When 2 people walk around a corner and suddenly see each other, there is an initiative roll to see which gets to act first and who's flat footed. But when invis is broken, the guy who was hit is never flat footed, he always reacts fast enough to get his dex mod versus the second swing.
It seems to me that a house rule should be made to have a little "mini-initiative' check between just the 2 people involved. I'd give an extra +4 to the one that was invisible too. If the attacker wins, the defender is flat footed to only that 1 attacker for the rest of the attackers action. If the defender wins, then the defender gets his full dex bonus and thus can't be sneak attacked a second time. Also, if the defender is engaged in combat with someone else at the time, I'd give him a -4 on his check. Someone with uncanny dodge wouldn't have to worry though, because he won't loose his dex bonus even if flat footed.