Is turning off my routers firewall bad?

I've had this problem where my Internet would constantly shut off but ever since I turned off the firewall on my router the Internet never goes off. Would it be dangerous just to keep my routers firewall off? Both my computers have there own anti virus and firewall and the only other devices I have are my iPhone, iPad, and Xbox 360

Yes, your routers firewall is the first layer of protection to your whole network. Without it you are much more prone to hackers etc.