Very dodgy but I had the same problem where after downloading the first free game I couldn't download the second. Turns out you need to follow the process below to get the 2nd game. IF I didn't know any better I'd be inclined to think Sony wanted to make it just a little bit more difficult to get that second game.
Q: I no longer have the option to choose my free Welcome Back games. What can I do? A: If you navigate away from the Welcome Back section of the store without choosing your free games or exit the store completely you may need to follow the below in order to choose and download your free games.
On your PlayStation 3 or PlayStation Portable navigate to the PlayStation Network icon on the XMB Log into your PlayStation Network account and choose Account Management > Transaction Management > Services List Choose “PlayStation Network Promotions” from the list of services displayed Select either “PS3 Free Games” or “PSP Free Games” and then choose “Select Content”
You will be taken to the store to choose your remaining free games.
PSA: Sony's Welcome Back package expires Sunday
Jul 3rd 2011 7:24AM (Joystiq)Q: I no longer have the option to choose my free Welcome Back games. What can I do?
A: If you navigate away from the Welcome Back section of the store without choosing your free games or exit the store completely you may need to follow the below in order to choose and download your free games.
On your PlayStation 3 or PlayStation Portable navigate to the PlayStation Network icon on the XMB
Log into your PlayStation Network account and choose Account Management > Transaction Management > Services List
Choose “PlayStation Network Promotions” from the list of services displayed
Select either “PS3 Free Games” or “PSP Free Games” and then choose “Select Content”
You will be taken to the store to choose your remaining free games.