So it's definitely not true that sailors drank grog (water mixed 3-1 with rum) because water would spoil -- they drank grog because alcohol was part of their rations and it was preferred to water.

That said, fresh water did spoil over time aboard ship, and a prudent captain would identify multiple watering places on a voyage, or use sailcloth or other canvas to channel rainwater into water barrels. In the time period I'm interested in, water was stored in wooden barrels, which were broken down into their component parts (hoops and staves) when they were not in use. So when ships needed water, they would anchor, send the ship's boats to a source of fresh water (usually a spring or river) with the cooper, reassemble their barrels, and fill them with water.

This process offers several points at which the water can be contaminated by microbes: when the barrels are broken down, when they're stored, when they're re-assembled, when they're filled with water, and so forth. It's also the case that in pre-modern times, rivers and streams could have contaminants in them themselves, and so the water that sailors were putting in barrels could come pre-loaded with nasty bacteria, which could multiply over time -- it wasn't purified or distilled in any way, except in very small quantities aboard some ships. So all of those factors would lead to spoilage over time.