The short version: your day-by-day analytics stick around for the life of the Link, with no expiry date.
What's kept long-term
Your loads, clicks, and unique-visitor counts, plotted over time, are stored for as long as the Link exists. Create a Link today and you'll still be able to open its analytics and see the full history a year (or more) from now.
What's recent-only
The detailed breakdowns (countries, devices and browsers, referrers) are built from a granular visit log we keep for about 45 days, so those reflect your recent traffic rather than the Link's entire lifetime. The over-time totals aren't affected; only the drill-down detail is time-limited.
Can I export it?
Not currently. Link analytics are viewable in the analytics tab, but there's no CSV export for them yet. We do offer CSV exports for song submissions and Hot or Not feedback, just not Links.
Anything that clears it?
Two things: deleting the Link, and hitting "Reset Analytics" on it (which is reversible). See the "What happens when I reset my analytics?" article for how reset works.