I know many companies have policies about storing source files on the network for backup purposes, which hasn't historically worked very well with Robohelp.
The following are my suggestions for Robohelp Classic, but which may still be valid for New UI, given your issues seem to be network related.
1. If you have multiple people working on the projects, I recommend using source control to store the projects. This means the project source is on the network and backed up, but you make changes on a local copy (and the check-in process copies your changes to the network, basically). I used to also recommend, for RH Classic versions, the local source control workspace be configured somewhere like "C:\Manuals", not inside your Windows User folder, as there were local paths stored in the source files that caused problems. I can't offer a recommendation in this regard for New UI, not having used it properly, nor with source control. Just keep it in mind if you go this route.
You can also use this method if there's only one writer, but I think only go this route for one persion if you have developers already using a source control tool, so you have technical support when something goes wrong. Troubleshooting when you have no idea about source control systems is a sure fire way to have a nervous breakdown. 🙂
2. If you only have one person accessing the projects, work on the projects locally, but upload a zip file to the network every night/week depending on how frequently you make changes, and after every production release. Have a good naming convention so you can identify nightly backups vs production releases, and go through regularly to delete old nightly backups. You'll need to make a call for your situation how much to keep - a month of backups or until the next production release, for example. You'll also need a policy for cleaning up/archiving the production release backups, depending on your corporate policies and disk space.
3. If you have multiple people accessing the projects but can't use source control for some reason, I still recommend working locally and storing zip backups on the network. Constant communication is the key for multiple people working on the projects. The backup principles are the same, but you will need to talk with colleagues constantly so you know who is working on what. I highly recommend that only one person works on a project at a time, and you download the latest zip from the network, after confirming with your colleagues that no-one else is working on it, or they confirm they have finished uploading their latest changes to the network.