Once the jar is opened, it may get contaminated, by anything suspended in the air, by cross-contamination ...etc.
- nutrients (your jam)
All of these will provide good conditions for cell culture (e.g. molds).
Make sure you keep it sealed properly and stashed away in a dry cool place.
Because there are no preservatives, there is nothing to prevent or stall
those unwanted elements from growing. Use it within a few days.
If you ever had fruits / bread grow mold at your place, that should give you
an idea on how long you can expect to keep it once opened before it goes bad.
E.g. black bread mold loves temperatures 15 - 30 C.