This question is likely to have subjective answers so I thought I'd throw my hat in
My (hiccup Uneducated) Opinion
- Yes, you should ask the user if he would like to again
- But only if he shows real engagement with the site and goes to it regularly.
- It should always be an option for him to do add it in the settings
Similarities
Adding a homescreen file reminds me a lot of rating systems.
Apps often remind you to rate them if you have been using them long enough. The consensus on this is that you show them an option to do something nice for us (the app makers) and for themselves (so Google can suggest better apps) at minimal disturbance.
Most apps do this after a while and most people are fine with it. In fact I'm pretty sure it leads to more ratings.
Here are some information on rating systems
- Rate Now, Remind Me Later, Never Remind Me Again
- Should I ask users to rate my app with pop-up window?