V. odd - milk supply does not turn on and off like a tap, any more than the blood supply.
However, let down can sometimes be a bit flaky - you have the milk but it makes itself unavailable.
I have come across women for whom this happens after a severe shock/distress - temporarily.
Serious illness may impact on supply, as well, but not a cold, and not wham-bam suddenly.
Babies can get colds too, and find sucking hard work.
I'd want to see what was happening before I came to any conclusion!