Hi There!
Thanks for the screenshots - they illustrate your question very clearly. Because I'm not located in Canada, I have to add your city name to my query rather then setting my location. When I search for 'Car Medics Elginburg', I am getting both of your locations, as in your August screenshot.
As to why you are no longer seeing this searching from where you are, it's important to understand that it's always totally up to Google whether they want to display one location or both. Some ideas:
1. It could be that they are only showing you the location physically closest to your mobile or desktop device. Have you tried taking your cell phone closer to the second location and doing the search from there to see if it is then showing as a single result, or as part of a double result?
2. Looks like you're not sharing phone numbers, so that's a good thing.
3. Looks like both businesses could earn some more reviews to make them a bit more powerful.
4. Here's something odd. From the Maps results, I'm clicking on the website link for your Perth Rd. location and am being taken here:
http://www.carmedics.ca/
This looks like a homepage, and rather than having Elginburg as the core city term you're optimizing for, it's talking about Kingston. Additionally, in looking up at your masthead, there appears to be NAP discrepancy going on. Your Google My Business data is:
1985 Perth Road
Glenburnie, ON K0H 1S0
vs. what is on your website:
1985 Perth Rd, Elginburg,ON K0H 1M0, Canada
So, is this business located in Kingston, Elginburg or Glenburnie? Clearly there is a discrepancy here of some kind that could be contributing to a lack of trust on Google's part in the data they have about your business.
5. Now I'm clicking on the website link for the Rigney location, which is also taking me to:
http://www.carmedics.ca/
It is not a best practice to have both GMB listings link to the same page on your website. You should have a unique landing page for each location and link your GMB listings to these instead of the homepage. These landing pages should be optimized only for their own NAP - without mixing in other geo-terms. They should feature strong, unique content and be linked to from a high level menu and elsewhere within the website.
In Sum -
You have NAP inconsistency going on for the Perth Rd. Location, and it's very confusing that both listings are clicking to a page talking about Kingston. More effort needs to be made to sort these locations out from one another and to be sure that NAP is consistently listed for each location everywhere it appears on the website, on GMB and on all citations.
Now, whether this will resolve the issue you are experiencing with only one location appearing is another matter. It's very important that you do the above work, but it still could be a user-as-centroid phenomenon you're experiencing on either desktop or mobile devices as you've got 2 locations in 2 different cities. Google may simply be choosing to show you the location nearest you, and I think it would be smart to test this physically with phones, bearing in mind that no 2 customers are guaranteed to see the same results. Their results will also be governed by their own physical location at the time of search, and other forms of personalization. Test both with phones with no geo-terms added to the search query and test with geo-terms added. See what you get.
What I've mentioned here is a start to troubleshooting. There could be other factors involved, but I really hope these quick thoughts help!