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• General/
• Harvest Moon: MM/
• Move Outs

I have yet to confirm the "MOVE OUTS" so this section will not be accurate.
Most people in the town can and will move out and become unavailable for you
to socialize. Only way to get them back is to ship the required items.

There are some ways that you can do to prevent them moving out.
1. Talk to them everyday, or at least once per two/three days.
2. Ship the items they need

Dia
SHIP: Herbs, and Pontana Roots

Tim
SHIP: Ores and Gems.

Basil
----- He will go away for the winter, and return when it's spring.
SHIP: Ship the herbs, and flowers if he went away in any season except Winter.

Nami
----- She will be there for summer only. Other seasons she's unavailable.

Gwen
SHIP: 10 Fish, 20 Vegetables
(Thanks Dark_Assassin_X, for the requirement to get Gwen back)

Gourmet
----- He'll be there for autumn only.

Carl
SHIP: Eggs and milk

Katie
----- She'll be back if Carl is back.

Louis
SHIP: Moonstones, Ores

Ray
SHIP: Fishes

Lyla
SHIP: Flowers, Berries, Fruits, Yarns and Good Clays

Ronald
SHIP: Fruits

Terry
SHIP: n/a befriend animals

Eve
SHIP: Strawberries

DAN
SHIP: Very Berries, Blueberries
 (Natsume told me that you need to ship the fishes, but two players shipped
  tons of the fishes, and didn't get him back. So the fishes don't work.)

So far, those characters are only people I know that can move out.