Hey @Radu Costea! Daniel from Customer Support Engineering here  

Are you opening the initial conversation, still seeing the button when you back out, then re-entering and leaving the conversation makes the button disappear? I can’t say I’ve heard of an issue like this and I don’t think there would be a reasonable cause. My best advice would be to first update your SDK to our latest version here, as we have had a recent update since your message was posted. Let us know if this resolves the issue If you can, please provide detail on the platforms this occurred on.

Exactly. If i go into the conversation and hit back again the send us message goes away. For now we will allow multiple conversations and its no longer a blocker. We did not tested this in a while since we disabled the single conversation option in messenger.