I got few steps to help you save your transactions in QuickBooks Online. To start, let's access your QBO account using incognito mode. Private mode prevents storing cache and cookies that might cause problems when running websites. Here are the shortcut keys you can use:
Google Chrome: press Ctrl + Shift + N
Mozilla Firefox and Microsoft Edge: press Ctrl + Shift + P
Safari: press Command + Shift + N
Once signed in, go to the +New icon and choose the transaction you'll need to create. When finished entering the details, see if you can find the Save button.
If this works, go back to your regular browser and clear the cache. This will remove the stored cache or cookies to refresh your browser. If the same thing happens,use another supported browser. It could be that the one you're currently using has a temporary issue with QuickBooks.