It went off in the bottle
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What the conditions actually are
A bathroom or kitchen, warm and humid, with the product opened repeatedly and sometimes contaminated by wet hands or a splash. That is a far harder test than a sealed jar in a cupboard and it runs for months.
Dilution weakens the system
A thin foaming formula or a customer-diluted refill has a lower concentration of everything, preservative included. A system that was adequate for the concentrate may not be for the diluted product, which is exactly where the refill proposition bites.
Natural preservation is harder, not simpler
Makers wanting to avoid conventional preservatives frequently end up with a system that has not been shown to work. The honest position is that this is a technical problem with a technical answer, not a matter of choosing gentler ingredients.
Signs it has gone
Cloudiness in a product that was clear, a change of smell, a film, separation, or visible growth. By the time any of those appear the problem is established, and it will be in every bottle from that batch rather than in one.
The container is part of it
A pump that draws from a sealed bottle is far better protected than an open-mouth container somebody dips into. One of the real arguments for a pump over a pour bottle in this category is contamination rather than convenience.
Hold product back and watch it
Retained bottles kept at a realistic temperature and opened periodically are how you learn what your product does over its claimed life. Testing only fresh product tells you nothing about month five.
Get the preservation checked rather than assumed
Challenge testing a formula is a laboratory service and it is the only way to know a system works rather than hoping it does. For a product that lives wet in a warm room for months, that is a reasonable thing to buy once per formulation.