A sourdough starter can typically survive unfed in the refrigerator for 1-2 weeks without significant issues. After that, it will become increasingly acidic and weak, potentially requiring multiple feedings to revive.
When you refrigerate your sourdough starter, you're essentially slowing down the fermentation process. The cold temperature significantly reduces the activity of the yeast and bacteria. However, they don't stop completely. They continue to consume the available starches and produce acids, just at a much slower rate.
Here's a breakdown of what happens over time:
To revive a neglected starter, discard all but a tablespoon or two, and then feed it regularly (every 12-24 hours) with equal parts flour and water until it doubles in size predictably after each feeding. This may take several days.
Before refrigerating your starter for an extended period, feed it well. A well-fed starter will have more resources to survive longer in the fridge. Also, consider freezing a portion of your starter as a backup. Frozen starter can be revived, although it may take a bit longer than refrigerated starter.