Is API use limited to one third party connection?

Is API use limited to one third party connection?

Hello,

I'm trying to connect two separate instances of a booking application to one Zoho CRM account, and it's working fine with one, but not the other. I've attempted setting it up using both the same Zoho CRM API key and separate API keys, yet still only one of the two booking accounts was integrating with Zoho.  Does Zoho somehow limit the use one API to only a singular third party connection.   Any insights / suggestions would be greatly appreciated.

Thanks,
Josh