If you are still having the issue then I would suggest that you take a couple minutes and drain the toilet tank so you can examine the ACTUATOR VALVE (the thing the flapper attaches too).
It sounds like your actuator valve may be cracked which would allow water to flow out too quickly and the actuator to drop too fast.
Otherwise, you could actually have purchased the wrong flapper....they have like 3 or 4 kind that fit this actuator valve. Here, go purchase another, thinner flapper (they make a thick one...could be you have that).
Finally, if all this doesn't solve your issue then you can try taping a quarter to the back end of the actauator valve and see if that helps keep the valve up longer (it should). If this works, you can use liquid epoxy to adhere the quarter permenantly, OK?
Check it out and let us know what you find.....I'm thinkin' cracked valve or wrong flapper disk!