If you have a BGP with them, it seems that either:
1. The BGP session is down
2. Bandwidth limit exceeded
3. Router ports flaps
4. Routing was dampened
Generaly, if the connection is capped, the router might drop the excessive packets and/or the BGP session is unstable, causing the port to flaps from the backbone's perspective. Depending on your area, if the session dropped too many times, the backbone might dampened the network routes.
<edit> However, this may not be the only thing that's causing it. It maybe something wrong with the Level3 router, or etc. Might want to check with them