Word for a rare astronomic event usable as metaphor for rare life situations

Once in a blue moon - refers to a very rare event.

To do something “once in a blue moon” is to do it very rarely: “That company puts on a good performance only once in a blue moon.” The phrase refers to the appearance of a second full moon within a calendar month, which actually happens about every thirty-two months.

Source: Dictionary.com

The planets aligning

It only occurs once in a thousand years like the planets aligning that a lady gets attracted to me and shows interest, but I ruin the opportunity (to approach her) stupidly and have to wait another thousand years!

This idiom will make those who believe in Astrology happy. The idea that the "stars" govern the fate of your love life is as old as romance itself.

Also, it's closer to the thousand year time scale you're looking for. So it would be slightly less annoying to astronomers than say Blue Moon.

A Blue Moon happens on average about once every 2.7 years. Occasionally two full moons will fall within the same month. The second full moon is also often called a Blue Moon, but this is not the term's original meaning.

google: how often is a blue moon

Astronomers can be pretty forgiving with big numbers but they get annoyed when you're off by orders of magnitude.

When astrologers speak of the planets being aligned (something which doesn't really concern astronomers) they don't mean that the planets will actually all lie on a straight line at some instant of time. One calculation of alignments within around thirty degrees (about as close as they can get) shows that the last such alignment was in 561 BC, and the next will be in 2854. The eight planets plus Pluto are somewhat aligned every 500 years, and are grouped within 30 degrees every one to three alignments.

When was the last time all of the planets were aligned? (Beginner) by Dave Kornreich

Here the number of zeros isn't off by more than 1. That may seem a bit sloppy but understand, the only thing that really stands a good chance of happening exactly once every thousand years is the earth going round the sun for the thousandth time.

If you really insist on sticking with the super-hyperbolic “1000-year” time frame, then you should go with something that actually does reoccur only that often (or something whose re-occurrence is at least “close enough for self-deprecation,” like Candied’s answer).

Personally, however, I’d reduce the time frame to either “once every 500 years,” which would render Candied’s answer totally accurate without detracting much from the impact of your hyperbole;

OR (and here’s my long-in-coming “answer”) else reduce the time frame even further to “once every 75 years or so” (or “once every lifetime or so”) and go with the fairly idiomatic:

about as often as Halley’s Comet comes around,

which, although a second sighting is possible in one lifetime, would still, I think, get your rather depressing point across adequately to most listeners/readers.
(example of usage from ‘Red Rum Comes To Light’ By Kansas Rae, via Google Books)

It only occurs once every 75 years or so, about as often as Halley’s Comet comes around, that a lady gets attracted to me and shows interest, but I [nearly always]ruin the opportunity stupidly and have to wait another lifetime or so [for it to happen again]!