First, you need to make sure that your wifi cap is not stopping the app from completing the download. So connect to an unlimited wifi source.
Second, try completely shutting off the phone. Hold down the power button until the slider appears, and slide it to turn the phone entirely off. Once it's off, start it up again. This might clear the problem.
Third, make sure iTunes on the phone isn't tyring to download something. Go to iTunes > More > Downloads. If it is, let it finish.
I don't know if it is possible to save the game data. It depends on how Beeline wrote the game. It may be possible to find the files on your phone by using a special app on your computer, but this can be very complicated.
If none of the above work, I'd try contacting Apple before giving up.
I've tried to update again with a unlimited wifi and this notice appear... https://m.ak.fbcdn.net/photos-h.ak/hphotos-ak-snc7/s720x720/403834_4191724214589 03_1053591102_n.jpg?dl=1
OK, if you've tried the things I suggested and they didn't work, then I think your only option is to delete and reinstall the app. It seems that this can happen when the phone gets confused about the status of the update.
If these apps work through GameCenter, it might be possible to recover your played state. I haven't tried it.
Also you might be able to recover your played state if you had backed up to a computer and turned on "Encrypt local backup". By turning on encryption, you allow your computer to save not just the apps but some of the data for each app, too.
In the future, you can avoid updating the app. It doesn't happen automatically, so just choose not to update it.
Sorry I can't be more help!
Yea, I have an iPod touch 4 gen. I was updating an app using a guest wifi when it halted halfway thru. Get a three bar connection and tap the app to restart the download. You may want to check the update details as the update may require a higher iOS or a newer iPhone. I discovered my update was not supported by a 4 gen iPod touch and by using iCloud I was able to recover the earlier version, but every device is different.