Is it possible to repair the twist-switch on the Maglite Solitaire?

Yes. You can get all replacement parts on ebay e.t.c.

Probably don't need anything in this instance.

These instructions will work for similar brands or makes of screw style torches with conventional or LED bulbs.

From my experience it can be, in order of most common:

1. Tightness. - Try taking apart clean the threads of dead skin, general dirt & metal on metal wear. You can use Isopropyl alcohol, screen cleaner or rubbing alcohol.
2. Spring Compression - Just pull spring in cap end out a little with some pliers to decompress the spring. i.e. make it slightly longer. Making better electrical contact.
3. Battery Length - Some are a couple of mm shorter than others. Accurately measure the old battery length against the new old.
4. Battery Low in Charge - Get a fresh one, quality battery some makes are choosy.
5. Electrical Contact - Clean off metal on metal contact where the top of battery meets bulb holder if you can take apart the torch completely.
6. Bulb Failing - Take out of torch. Inspect the bulb carefully. Can you see a broken filament? Replace new bulb.

# Fingers crossed if you follow all these in order you should have a working torch for many years longer. yeh! Give me a thumbs up. Many thanks in advance ;)