Word for a source of mental-strength

I like the word "Inspiration" for that.

Edited to include the word "epiphany" at the request of the original poaster.

It's a bit esoteric, but one possibility is tonic. Its concrete connotation is medicinal, similar to elixir, but dictionary.com also defines it as "anything invigorating physically, mentally, or morally".

1) Jenna is a middle-aged woman, fighting cancer, her situation is really hopeless, she doesn't think living is worthwhile, but then she thinks about her baby, who's still very young and needs his mother to help him find his feet in the world. This gives Jenna a reason to persist in her cause to fight cancer for a little longer. The boy becomes her tonic.

2) Arthur, plays as a striker for a football club. His team are mid-way through their match with their local-rivals, and haven't scored a goal yet, they know if they don't win the game, their cup-run would be over, Arthur sees the look on his team-mates and the coach, they're all looking very glum. This invigorates Arthur, albeit paradoxically, to give in his best. He scores a goal and his team win the match. The look on his team-mates' faces was Arthur's tonic.

Another possibility is stimulant. Relative to tonic, it is more superficial and immediate, and does not imply the existence of a problem.

Another possibility is buoy. This one does not actively inspire you to act, merely keeps you from drowning in despair.

The best term I can think of next to inspiration (which has already been suggested) is beacon.

Another possibility is muse, which is roughly synonymous with inspiration and is especially used to denote a guiding genius. Also, pillar.

She was an eternal beacon.

Steeped in both dance and Latin culture, she was my muse.

When everything looked hopeless, he was my pillar.