EDIT:
I was wrong. I'm completely updating this post, thanks to SteveInWA's thoughts.
After extensive testing, the problem turned out to be my all-in-one multi-function printer/fax/scanner, from the HP OfficeJet Pro L7500 series.
I brought the Obi to the same room as the printer/fax/scanner. When I connect the AiO directly to the Obi202 line 1 jack using a 6P6C or 6P4C wire, the flashing LEDs and red LED reset occur on the Obi box.
But when I plug in a 6P2C wire in the line 1 jack and connect it to the printer-fax line jack, this does not occur and it functions normally.
(The telecom distribution module in my house wiring panel was merely passing along whatever problems were introduced into the line by the HP fax machine. And since the fax machine was connected to the telecom distribution module by 6P6C wire and Cat 6 Ethernet, as soon as I plugged in the Obi to the distribution module by 6P6C or 6P4C, it received the problems being sent out on those twisted pairs -- but not when I connected it by 6P2C.)
I bought another multi-function printer/fax/scanner, an Epson WF-3640, and it does not produce this same problem, even when connected by 6P6C or 6P4C wire to the Obi line 1 jack.
Also, the problem apparently does not happen with the line 2 jack on the Obi even when connected by 6P6C or 6P4C to the OfficeJet.
I'm unsure at this time whether this is a design issue with OfficeJet Pro L7500 series MFPs or whether this problem is specific to the MFP I own.
Thanks to Steve for the feedback.
This is an FYI to people setting up Obihai boxes:
If you use the type of standard telephone wire that has six contacts (that is, wires or colors visible) at the plug -- called 6P6C -- and connect it from your Obi's Line 1 or Line 2 jack to a telco distribution module (the type found in homes built since 2000) in your wiring panel, the Obi will fail.
At first, the Obi's Line 1 and Line 2 LEDs will flash green. Then after about 10 seconds, the Obi will reset itself. The power LED turns off, then goes solid red, then flashes green, then goes solid green. The Line 1 and Line 2 LEDs flash again, unless you remove the 6P6C wiring from either the Obi box or the distribution module. If you leave the wiring connected, the reset process happens over and over.
This problem is specific to 6P6C wiring (sometimes known as RJ25 in other situations) and telecom distribution modules.
I tested this with two different brands of 6P6C wiring from different manufacturers and it happens with both. Both wires are known to be good, as they work perfectly between regular telephone handsets and wall jacks.
Both wires also work perfectly between the Obi202 and telephone handsets directly.
The telecom distribution module itself works perfectly, and distributes the telephone connection from either landline providers or VoIP providers like Obi perfectly (once a 6P2C wire is used to connect it to the module).
Once 6P2C wiring is used to connect this Obi202 to the telco module, this Obi box works properly.
So, in summary, do not use 6P6C telephone wiring between your Obi box and a telephone distribution module, until Obi engineers fix this problem.