I did the following two experiments as HartleySan suggested.
1. I created an HTML file that had the JavaScript in the same file, and the JavaScript just invoked an alert. This worked properly on my Mac and also on my iPad; I could see the alert on both devices.
2. I then moved the JavaScript containing the alert to a separate .js file (in the same directory as the HTML). This worked properly on my Mac, but it did not work on my iPad. I could see the alert on my Mac, but could not see it on my iPad.
So, this suggests that something is not right when using the Dropbox app on my iPad to view HTML files that refer to a file path for a separate JavaScript file.
3. I also did the following experiment, similar to what I did a couple days ago. I did a "copy public link" of the HTML file that had the JavaScript in a separate file, and I opened this link using Safari on my iPad. This time, the alert did appear when viewing the web page on my iPad.
So, this means that, under certain circumstances, such as in test #3, the file paths do work properly for files contained in Dropbox when the web page is directly viewed using Safari on the iPad, and is not accessed through the Dropbox app. But in test #2, the file paths do not work properly when the web page is accessed through the Dropbox app on the iPad.