nuvi 3597 not showing osm custom maps

Were those OSM maps working before the firmware update?
When the Nuvi is plugged into the PC does Windows Explorer show the SD card and the maps being present.

When adding maps to an SD card they MUST be present in a Map folder in the root directory.
If they are not in that folder create a Map folder and move them there.

My 3597 is on the most current firmware and custom maps, including overlays, display as in the past.

All custom maps are in the file gmapsupp.img, in the directory called garmin, on the SD card.

I realize the 3597 will recognize a map named gmapsupp.img on an SD card in the Garmin folder.
However, the OP stated he has custom OSM MAPS on his SD card. Multiple maps must be located in the Map folder on the SD card and you may name them anything you wish.

I may not be interpreting your statement correctly, "All custom maps are in the file gmapsupp.img". Unless you combined several maps into one and named it gmapsupp.img, you cannot have several gmapsupp.img in the same folder.

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Before the firmware update ... I am not sure which would be the last one I applied that changed the behavior - I had individual maps in the MAP folder in a SD card. When I would check the maps all of them showed up. I can see them with explorer. But after I updated just recently the nuvi does not see them. I only use these maps when I travel and the last time I used them was around early January and they worked fine. Is Garmin pushing us to use only their maps?

Another strange behavior> I live close to the Mexican border. Sometimes I travel to Mexico and I use the Garmin maps without problem. But after the update, I can no longer route from the U.S. into Mexico. The Nuvi stops its route calculation at 80%.

Check what is provided on your unit by looking up the model number. The 3597 has several different models, so you need the the model of your unit. Not all came with Mexico maps.

As Box Car indicated, did your Nuvi 3597 come with Lifetime Updates with the full North America map?

To get Mexico in your Map Info screen it should display CN North America NT
2015.20 ALL

Also what OSM maps do you have on the SD card?
If you have overlapping coverage of the same are they may not appear in your map info screen.

Why don't you remove the SD card, then check if you have the North America ALL map. If you do, now see if you route to Mexico.

Also to see if there is a map conflict, without the SD card inserted, uncheck the North America map in the Map Info screen and shut off the Nuvi.
Next insert the SD card with the OSM maps and turn the Nuvi on.
Do the OSM maps now display in the Map Info page?

If they show, there is a conflict with the OSM maps. Remove the SD card and check the loaded CN North America map again to have it operational.