Can I recover lost app data after restore?

Hi everyone and thank you in advance to anyone who can offer some help!

Apple recently told me some issues I was having with my phone were software based and they refused to issue me a replacement phone until I attempted to setup the phone as a new phone in iTunes. I did so and it didn't fix the issues. I am waiting on a replacement, however, in the meantime, I am restoring to the backup file from iTunes. I have restored all of my general data but, all of my app data is missing.

I'm most concerned with an app that keeps track of my time off requests for work (including info on all of my vacation days and sick time, from the last 5 years) as I know I have time to take off before the end of the month. I know, it sounds silly.

Bottom line, is there a way to restore the backed-up app data to my phone? I've never had this problem when I've used the backup to set up a new phone or a replacement in the past.

Many thanks!

Note: I have an iPhone 5 and am using a Windows based computer.