You should only have to tap a pokemon once to start a catch attempt.
There are possible issues you may be encountering, if tapping once does not initiate a catch attempt:
Network Issues: If the game is having problems communicating with the server, it may be unable to confirm your selection. As a result, your taps may not be validated, and will in turn not register as actual input. This is especially an issue so close to launch, as the servers are constantly being overloaded.
GPS Issues: Once you start catching a pokemon, location does not appear to make a difference. However, you still need to be within proximity of the pokemon, to initiate the catch attempt. If your GPS is experiencing any issues, it might invalidate your proximity to the pokemon. In turn, your game may think you are not close enough to catch the pokemon, and reject your input.
Game Bug: Pokemon Go is still very new, and there are a few game-breaking bugs that have been found, but other users. Even for a game that has been through considerable beta testing, it is common for bugs to pop up on release, when there are many more users playing. If you find no other possible cause, it would be a good idea to submit a Bug Report to Niantic Labs. There is no guarantee they will deliberately respond to you, but if it confirms to be a bug, your report will help towards a quicker resolution.