-- https://wallet.bitcoin.com/
It seems like the latest version is 5.2, which you can download from here. https://github.com/Bitcoin-com/Wallet/releases (Or simply click the link above.)
I'm not sure how exactly Bitcoin.com handles the updating process/whether or not your wallet files will be saved. To be sure, i'd recommend to make a backup of those files before downloading the new version (By exporting the current wallet.. (Although it's quite unnecessary if you have your seed.)
If you're referring to a wallet export from the Settings > Wallets & Integrations > More Options > Export Wallet screen, you can copy your wallet's keys (private and/or public) to your clipboard for pasting into a text file on your device, or for pasting into an email.
If referring to when you are shown your backup words on the screen when it shows "Your wallet is backed up", it is not backed up to a file; it simply means that - by entering the phrase - you have shown that you have backed up your wallet by virtue of memorising your backup words or writing them down somewhere safe.
Once you have your seed words your wallet is backed up.
Fremont
If they don't save your wallet files, you should probably try to import the Backup Seed into the wallet.