In short
Almost always it's one of three things: the SMS credit balance ran out, the alert's trigger genuinely wasn't met, or the mobile number on file is out of date.
Alerts fail silently by design rather than emailing an error, which is convenient right up until the one time you were relying on it. These three checks cover nearly every case.
Check these first
Each text costs a small amount of prepaid credit, and once the balance hits zero, alerts simply stop sending rather than showing any warning, so a quick look at the balance on the Alerts page is always worth doing first. It's also worth confirming the alert itself is still turned on rather than accidentally removed, and that the mobile number saved on the page is current and able to receive texts, a stale number after a phone change is one of the most common causes.
For Wind Alerts specifically
A Wind Alert only fires when the live reading at your chosen station actually crosses the exact threshold you set. If the wind sat just under it, or your launch spot simply reads differently to the nearest station, no text is the expected outcome rather than a fault. Nearby Observation Stations is a good way to see the wider pattern and judge whether your threshold or station choice needs adjusting.
Still stuck
Contact Feedback and mention the alert type and roughly when you expected it, and it can be checked from our end.
Related reading
See How do SMS Wind and Forecast Alerts work? and What can Nearby Observation Stations tell me?