The free 000webhost limits the number of requests you can receive before temporarily blocking your web site. In other words, if you get too much traffic they temporarily disable you.
I don't know if it's a tactic to prioritize paying customers, or just one to make you switch to paid hosting, but either way you can't expect a free web host to give you that much bandwith, disk space and cpu usage for free.
Deep Thought, you might have to paid hosting, or use a second web host to cool off a bit of the traffic from 000. Or leave it as is, it's your choice after all.