i keep getting stuck on the software update page on my apple watch saying software is up to date

Hi

First update your iPhone to the latest version of iOS (start by making a backup):

Update the iOS software on your iPhone, iPad, or iPod touch - Apple Support

Then update the software on your Apple Watch by following the remaining instructions here:

Update the software on your Apple Watch - Apple Support

If necessary, unpair your Apple Watch and then re-pair it (watchOS will be updated as part of the process):

• The Watch app on your iPhone takes a backup of your watch automatically when unpairing via the app. Choose to Restore from Backup during set up. Most data and settings will be restored, with some exceptions (eg Apple Pay cards, passcode).
• Unpair your Apple Watch and iPhone - Apple Support
• Set up your Apple Watch - Apple Support

i saw this happens on 2 apple watch,and the way i use to fix this issue is 100% successful.

follow this steps:

1. update your iPhone to the new update, now is IOS 10.3.1
2. restart your iPhone (this is the step you have to do)
3. open watch APP on your iphone,and see if it may up to date. or it won't,you have to unpair your applewatch.
4. restart your apple watch and pair it with your iPhone .(it will be work for now)
5. btw,better connect your iPhone and the apple watch with the charger,

You may need to restore your Apple Watch from a backup

Unpair your Apple Watch and iPhone - Apple Support

Here is an article on how to repair and restore you Apple Watch from a backup.

http://www.imore.com/how-restore-your-apple-watch-backup