Some users say that is happening because of a PIN Lock you use. So to fix Absinthe icon white screen or white page, is deleteing email account and then disabling the PIN lock and then re-run the jailbreak, afterward Set VPN toggle to ON mode. That should fix the Absinthe white screen.
And alternative solution, albeit the above is reported to able to solved problem for some users, but there are others who didn't make it. So the alternative solution is.
1. Without deleting email accounts, but still disable PIN,
2. Close the Absinthe app, then rerun it,
3. You will see another white screen but don't panic, now set VPN to ON, then reboot,
4. Aha! Cydia shows up now.
5. Means your iPhone 4s is jailbroken!
Via: MacRumors Forum.
And if you are experiencing the white icon errors on springboard after jailbreaking iOS 5 with Absinthe, the fix is simply pick one free application from Cydia, install and then run it. This should fix the problem temporarily. However it is recommended to re-jailbreak your A5 device, as the Absinthe is recently updated to v0.2 that supports Windows too.
Anyway have download Absinthe 0.1.2-2? And jailbreak iPhone 4s, iPad 2 untethered using Absinthe?