iPhone app could not be installed at this time

clear your cache and cookies in Safari, make sure your device is in provisioning profile and provisioning profile is installed on the device.

If everything mentioned above didn't help, try to create a new build with higher build number and try to distribute your app again

Most common issues that cause this are (from testflight's website):

• Device storage is full
• The provisioning profile is a developer provisioning profile
• The ad hoc distribution provisioning profile is corrupted and the device is having an issue with it.
• The device was restored from a backup and is causing a conflict for over-the-air distribution
• There was a network timeout
• Architecture settings of the build and the device are incompatible ( can sometimes happen -when "Build Active Architecture Only" is on when building).
• Not Using Mobile Safari.

for me it turned out that my client's ipad was running iOS 4.2.2 and my project supports 5.0+.

Recently default Xcode project settings set ONLY_ACTIVE_ARCH (Build Active Architecture Only) to yes for Debug configuration.
So your build can not be installed on different hardware than the one you use for development.
Change this setting and installation should go fine.

As for Xcode 5.1, the problem was in arm64 architecture in VALID_ARCHS. Building the release configuration for 5.0 device locally gives the following error:

Xcode cannot install or launch applications supporting the 64-bit architecture on devices running iOS versions prior to 6.0. This configuration is supported for distribution through the iOS App Store, but cannot be used during development with Xcode. To continue, edit the Run scheme action and select a build configuration that does not include the 64-bit architecture.

Removing arm64 from VALID_ARCHS solves the issue. In my case I had to create a separate branch for testing on iOS 5 devices.