After about 8 half-lives, the remaining amount of C-14 (if there is any remaining) is too small to be measured.
For this reason, it is simply impossible for carbon dating to give dates as old as millions of years. Closed systems, void of any contamination and without loss of the parent element (C-14) or daughter element. Known amounts of parent and daughter elements present from the beginning. If the decay rate of C-14 were not always constant, then this would be devastating to the technique's credibility.
With this said, it would be worth while to check out this feedback session which does seem to suggest that there might have been an accelerated decay rate in the past, at least for the uranium-lead method.
“It is important to realize that an accurate radiometric date can be obtained only if the mineral remained a closed system during the entire period since its formation.
For this reason, I will have to bite the bullet and accept that it is reasonable to assume the decay rate is constant (even though I give this assumption, this doesn’t mean the decay rate is constant.