36 volts you say? hmmm.. ok

ok, keep in mind that a BMS on a LIFEPO4 battery will shut down if a) it reaches critically low voltage or b)too much amps are drawn all at once (i'm basing this on what i've lived, for more detailed info, you may want to contact a LIFEPO4 expert)

it would be good to know what your controller is rated at, and the same for your motor... that way you can get replacement battery and controller if necessary.

what i was about to propose is slighty costly but it will definitely lead to a resolution. it's called scoping the problem by replacing parts for knwon good components.

i.e you want a known good battery and put in instead of your existing one
same goes for your controller

this is what i would have done in your place.. and if i replace the battery and the problem goes away, then i know it's my battery. see? i told you i was not electronic genius, this is simple troubleshooting 101 for those who don't mind spending a little.

that experiment may cost ya around 500 bucks (notice the use of ya instead of you, that's meant as a suthern accent, i use it whenever i talk ridiculous money )

but.. if you get a cycle analyst and limit the amperage, that may be less costly as a first step in resolving your issue. these analyst run you around 120 bucks US or so. i got one and i honestly tell you that i can't imagine operating my bike without it. now here's the catch, in order for this analyst to work, it needs to hook up to your controller... so you know where i'm going with this. you'll need to lookat your controller. www.ebikes.ca not only sells these analysts but they actually build them. they are great folks, i would contact them if i were you and get into a convo with them about the types of connectors you have on your controller and see if you can fit one on.

for those reading this, please don't fry me for my proposition of replacing parts as a means of troubleshooting... i come from an I.T. background, and that's how i normally resolve issues, i tackle the probable causes by ensuring i have good components at hand to swap, so you can imagine i have more than one pc at home etc, for that reason, one pc goes down, i open it up, suspsect it's this or that component, i swap parts, whammo done.