My GPSMAP H1 is continuously rebooting.

From Garmin's own change log for the GPSMAP H1/H1i Software Version 6.04:

• Updated tracking and activity recording to auto-resume if the device crashed

This doesn't exactly give (me) much confidence or trust in the device.

If it were just occasional crashes with a restart, it would be annoying but manageable. What’s happening here is that the device becomes unusable! Even more serious, considering that it becomes impossible to send an InReach emergency request, which I have a subscription for.
A disaster never seen with previous devices.

That is exactly what happend to my H1.  It went into never ending reboot cycles making it useless to navigate. I could not reset the device myself. It was returned to the Garmin factory and only they could reset the device.  still carry a smartphone with locus map for this reason.

I managed to get the device working again!
I connected the USB cable to the computer and, during boot, held down the UP button; after about 30 seconds the device enters USB mode.
From the computer, I renamed the .IMG extension of all the maps in the GARMIN folder of the internal memory so that they are not recognized (they can be renamed with any extension or even without one; I renamed them to avoid deleting or transferring them).
I then disconnected the cable and rebooted the device—everything works! The base maps are missing, but all the custom maps stored on the SSD work correctly.
It is likely that the crash was caused by one of the original preloaded maps, but I did not run further tests to identify which one.

The major issue and concern at this point is the device’s reliability.
If this problem were to occur during a hike, it would be impossible to perform this recovery procedure.

I also managed to start the device; I entered mass storage mode, deleted all files, and reinstalled the maps using Garmin Express.

​It is quite concerning that it’s impossible to recover the device from a bootloop without a computer. Since this is a brand-new device, bugs are understandable, but a device intended for emergency communication should not behave this way.

Anyone still having this issue with firmware 6.04 installed? After removing the microSD card and all third party maps?

I had the rebooting issue 4 times. Even without installing third party maps. Last time, it was a with the H1 tracked activity that caused the issue, combined with a power off. Had to clean all data and a firm reboot plus sync with Explore on my iphone to restore courses. Now i am navigating with my Fenix as the H1 is unreliable during my 5 days trekking. I would strongly advice not to rely on the H1 for wilderness trekking. And buy the inreach mini as a separate device in case of emergency. 

With FW 5.09 and third-party maps installed on the SD card, there were other bugs, but never continuous rebooting. It had never happened to me in about twenty days of use.
With the device in the same condition and only updated to 6.04, on the first hike I noticed that the track I was recording was not displayed on the map.
When I tried to set “color” and “show on map,” continuous rebooting started, with no way to exit it even with a hard reset and after removing the SD card.
At home, with a USB connection to the computer, after renaming the maps and the Activities and Courses folders in the internal memory, I finally managed to get out of it and the device restarted.
The operation that had caused the continuous reboot now works without problems, but how reliable can it be?

I am not sure what exactly triggered a bootloop on my device.

Earlier that day, I planned a course directly on the device and followed the route. Unfortunately, during navigation, whenever I went off-course and the device tried to recalculate a new route, it usually failed, stating it was unable to find one. I couldn't force it to recalculate successfully; the only way to fix it was to select the destination again and start a completely new navigation.

The bootloop occurred after I had already returned home.

From what I’ve read, Garmin recommends planning courses via the Explore app. However, the web version lacks a routing engine, and the mobile app requires an internet connection for routing to work. Since the device itself supports offline routing, I am looking for other options. Is there any way to get offline routing functionality other than using Locus Map and BRouter?

I’ve found that keeping the internal storage out of the box with only the factory installed maps is the better way to go. Any additionally purchased Garmin downloaded or 3rd party maps always go on external SD storage.

If you end up downloading to internal storage you can of course move them over to the SD card with it out of the device and in another slot on your PC. It’s faster that way.

As far as 3rd party maps (and especially routing software), you’re kind of on your own to experiment. I don’t have any issues or restrictions with Explore or Express and I’ll probably use BaseCamp till the day I die so I’m not at the same risk of corrupting/bricking anything.