Could competitive flow reduce internal thoracic artery graft patency?

Absolutely. It can happen. If the vessel that is bypassed has significant flow, the mammary artery can fail.
Yes. If the internal thoracic artery is used as a bypass conduit to a vessel that does not need a bypass, like one with less than significant blockage, or one that has adequate collateral flow to it, the bypass graft will gradually become atretic (small) and eventually shot down. In rare cases, it will close rather quickly in the immediate post-op period. This is not a common occurrence thankfully.

Related Questions

Could bilateral internal thoracic artery grafting increase surgical risk?

Yes. The use of bilateral internal mammary arteries can increase the risk for decreased blood flow to the sternum (breast bone) and increase the risk for wound infections and lack of healing or fusion of the sternum. Read more...
Not always . There is some evidence that in diabetic patients it can increase the risk of eternal wound infections. Not in non diabetics. This increase risk in diabetics has been debated and there is some recent data suggesting that it may not be true. Read more...