Answer: Amaryllis are tender rather than hardy bulbs. As such, they will not survive freezing temperatures.
Since they are bulbs, they are cyclical growers. They will bloom, then grow as foliage plants to rebuild the bulb, then go dormant, then bloom again. In order to keep the bulb strong enough to bloom again you need to treat the bulb carefully during the foliage stage. Treat it like a prized container plant, feeding it and watering it regularly so that it growes vigorously and produces lots of good strong healthy leaves. This sturdy healthy leaf growth will feed the bulb and in time it will grow large enough to produce offsets which can then be separated and grown on their own.
In my experience, it works well to set the pots outdoors in semishade for the summer, then in fall (before frost -- they are not hardy) bring them indoors and stop watering to dry them out so that the leaves turn yellow and die back. I remove the leaves when they are completely crispy, and let the bulbs sit in a cool but not freezing space for about 8 weeks or more. After the "rest" I water them lightly and wait for them to send up new growth and start the cycle all over again.
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