I apologize in advance if I am not more specific to the trouble you are actually having. I offer the following only if it might ring some bells for you or others on what might be at issue.
It is good you can create and delete some webhooks. You might try to use CLI and list your webhooks so you can actually record what you have in case they become unavailable for whatever reason.
A while back (last fall), I was having what seems to be similar trouble with my webhooks. The integrations page would wig out on me. It turned out, the solution for me, was to clear out the mess of poorly formed web hooks I had been using, over time. There was close to the maximum number of integrations in my account. I know because I was trying to add more and could not. I recall reading a thread where @ScruffR commented about the use of a prefix in an event and responding to it with just ONE webhook instead of several (could not find thread, sorry). Well, that was my problem - several webhooks using the same prefix (or, whatever else I had coded in them). I reduced the number of webhooks from 20 down to 3. Every thing worked as expected. Also, the integrations page stopped jumping around! 
I did see this thread about multiple webhooks firing from @rickkas7 :
https://community.particle.io/t/webhook-firing-twice-in-a-row/61125/2
Hope this helps!