UM … There’s a read-only mode you can enter by shutting down, ejecting the disk pack, booting, & hitting CTRL+ALT+SHIFT+R to toggle, and shut down again to reinsert the disk pack… Google seems to suggest that in some instances that has cured a boot loop, I’m not sure how much credence I give to the procedure. I guess you might try it, not sure I personally would without support suggesting it.
Trouble is I can’t think of many other options to rescue data before trying things like a factory reset (with associated data loss). There’s companies that sell data recovery software, such as UFS Explorer… or ReclaiMe Pro (neither of which is free or even particularly cheap) which may or may not allow you to recover your data before such drastic action, assuming you have a way to attach that number of drives to your PC, or else there’s scour the market (new or used) for a replacement unit & hope …
There’s no guarantee support can help either, but there’s a choice to be made between gambling on other possible answers, or paying & maybe getting a solution, or maybe being told you need to gamble on other solutions / data recovery software or (expensive) data recovery labs.
Ideally I’d be saying, “try a factory reset/wipe, if it succeeds, restore your backup, if not, replace the unit & restore your backup”.
I’m hitting the limits of what I can offer by way of suggestions at this point… 8 times out of 10, reboot loops seem to be PSU issues… if yours isn’t I’m getting short on new ideas.
IRL if anyone asks me about NAS units (Drobo or other) my response is “Budget for TWO so you can replicate/backup one to the other… RAID is NOT a backup NEVER rely on it.”
Edit: you might get more answers if you also post on reddit r/drobo though I won’t be able to add anything more than I’ve said already, though to be fair, that tends to be just people complaining that Drobo is no good & suggesting people migrate to other solutions, regardless that Drobos are actually no less reliable than many other solutions, however other experienced users exist there who don’t post here. The same might also be true on spiceworks.