Matt Taylor said:

I am not convinced by the remote desktop approach. When Sage becomes unstable and gets stuck in a processing loop I need to speak to the IT supplier to force close my application. It also creates some annoying workarounds for downloading data and reports from the remote desktop to our machines, or uploading attachments to Sage from our machines.

That sounds like you are using a 'Remote Application' rather than desktop RDP session. That being the case you are correct that it means there are some technical limitations as you do not have full desktop access. You could ask your IT company to allow the remote app to access local drives, which would make it a lot easier to download reports or upload attachments. You could also ask your IT company to provide desktop access instead of/as well as the remote application that would allow you to 'self serve' and resolve issues if the application hung for some reason. Publishing the full desktop could solve a number of your issues but, even with that in place you'd still have limitations and some features such as 'Send To Excel' would still not work, unless Microsoft Office were installed/licensed on the remote server(s). It's essentially technological limitations you are hitting up against.

Matt Taylor said:

I am looking at various suppliers that appear to offer 'cloud hosting'. In my mind this would mean the software was installed on our machines and all data was held securely in the cloud, with no sync issues if multiple users were logged on at the same time.

You might want to consider the Remote Data Access feature (see this link for details https://my.sage.co.uk/public/help.aspx#/customer/support/accounts/hub/working-remotely/guides) which would be close to what you are envisaging. Remote Data Access is already built in to Accounts and allows you to share data online so you can connect to it through the application using a secure Internet connection. In this setup you do still have a copy of the data locally, but it is synchronised to the cloud allowing you to connect to, and use that data from another location (the Accounts desktop application still needs to be installed at the other site). 

It's not 100% what you are envisaging but is probably the closest there is. There is no solution where the software is installed locally and data is only held in the cloud. We do of course have a 'cloud native product https://www.sage.com/en-gb/sage-business-cloud/accounting/ where both the data and the application are in the cloud, and you simply use your web browser to connect. However it is worth noting that it does not have all the features that our desktop product does so you would need to confirm if it covers all the features you currently need/use.

Matt Taylor said:

What I am wondering - and am hoping others can provide their thoughts on - is whether this 'cloud hosting' tends to be remote desktop via another name or something else?

There are a few providers out there offering a hosted version of Sage 50 Accounts, including some that also provide Microsoft Office alongside it. But any provider offering cloud hosting for Sage 50 Accounts would come with similar limitations as your current setup. There is really only the option of publishing a remote desktop or a remote application and both come with pros and cons, most of which apply to any application delivered in this manner and are not specific to it being Sage 50 Accounts. Unfortunately the same is true if you 'self host' and publish your own Remote Desktop/Remote Application from your own local server and connect to it via a VPN. The advantage of that approach is you have much more control over what you can/can't access and you do not introduce potential latency issues as the data would be held locally. This approach would also not fulfil your desire to have the data stored securely in the cloud so if that is a key requirement then a hosted desktop/app, or migrating to a native cloud product really are the only choices.

Hope that helps