The problem with automatically saving it is that you could end up in a situation where the icons get scrambled up for whatever reason, and then the auto-save overwrites your good locations with bad ones.
If you want to save it automatically still, you can create a Custom Function and Trigger rule to do that. Please see the attached screenshots for reference.
And if you assign the profile to a Monitor Profile, it will auto-load whenever that Monitor Profile is detected.
Hope that helps!
CustomFunction.png
TriggerRule.png