The most common problem stems from the intuitive reaction to hold the(after all, in most arcade games such controls would be expected). However, as Astro Chicken information screen tells you, toggles flapping. Thus, the best way to succeed is to hit it once and wait for the chicken to cease descent before pressing it again. Similarly, using , and buttons implies a single hit of a direction key to prevent mixed messages.
Most players prefer to turn down the speed setting of the game as low as possible. Even the game's original hint book lists this as the only strategy to this minigame. However, with the speed setting set to an all time low, you face the problem of delayed response. This often leads to superfluous key presses which sends mixed messages to your poultry avatar, making him much less responsive than necessary. Although there is no one correct setting, values around 6 and slower are recommended.
The game gives you more feed than necessary to land every chicken. Most of your deaths occur due to a "bug," in which the chicken will bounce up and down on the platform in an uncontrollable succession until death. Even if such behaviour was implemented by sadistic design, at times it can not be avoided. Keep in mind, that it does not happen often enough to get in the way of landing 10 chickens with just one buckazoid.