I have been asked several times why feeding should be over with by Oct 5th.
That date is just a date I always tried to shoot for to finish feeding. I know that the later it gets the bees can become reluctant at taking the syrup as it gets colder.
A beekeeper can feed into late Oct. but consider this. Feeding stimulates brood rearing. The later a hive is fed there will be brood hatching out a minimum of 21 days after the feeding is done. The bees have to keep the brood at a higher temperature so they will eat more of their winter stores. Also Varroa will still be increasing their numbers if brood is still being raised. The bees have to convert the sugar syrup to honey.
All of this takes more effort that can be prevented by finishing by early Oct.
If a hive needs to be fed then of course feed it. By putting two feeder pails on at once can get the food in the hive faster and not drag the feeding out another two weeks.