I'm assuming that you're using Windows 10, because I've run across this problem myself. It's maddening, because I've run across it even when I haven't had the program open.
There are usually two factors involved here; one due to Adobe temporary files and one due to the vagaries of the Windows operating system.
The Adobe factor: When you open a file in Adobe graphics applications, you actually have two files — your [named InDesign file].indd and a second, [Buncha letters and numbers].tmp file. That .tmp file is the one on your screen you're modifying. The .indd file is the one you opened and is saved on your hard drive. There are a number of reasons why this may cause conflicts — working with remote/virtual cloud services, previous .tmp files not shutting down after you save/close the files and polluting your system, etc.
If you can live with having two files for a moment, you can use the File>Save As... menu command to save the file to your external drive. That should get your document file over there fine. Then, to make sure everything is fine, go open the file on the external drive, work with it a little and then save/close it in the location on your external drive. It should work fine.
The Windows factor: One of the great things about working with Windows File Explorer is that when Windows recognizes the file format and the related application is installed on your system, the Preview pane gives you a little thumbnail view of the associated file — by either showing the program icon associated with it or a small view of the actual file. But when it isn't working right, Windows "protects" that file, assuming that there are two copies of the file open — one in the Preview pane of your File Explorer window and one in your Adobe application. And if you double-clicked on the file in that File Explorer window to open it in your Adobe application, Windows gives the Preview pane image gets first dibs. And your file in the Adobe application loses out.
Getting past this issue is as easy as closing the Preview pane. Go to the View tab in the File Explorer window and click to de-select the Preview pane button to the upper-left. This should eliminate the Windows factor.
Hope this helps,
Randy