can maple syrup be refrigerated after it was out for a few days?

Unless you left it open to the air it should be perfectly safe. Maple sap is thickened into syrup via boiling so any bacteria/etc. originating in it will be killed off.

Thick sugary syrups also make it very hard for bacteria and mold to grow. Despite the plentiful food source, the concentrated sugar is dessicative:

OK, maple syrup is wet, but it’s also extremely high in sugar. All that sugar has the effect of pulling water out of cells, and the vast majority of fungi can’t grow in maple syrup at all [...] maple syrup typically has a water activity of about 0.87 to 0.88, pretty hostile to most molds.

Syrup doesn't have the other nice properties honey that make it virtually immune to nasties, though, so I wouldn't continue to leave it out. If you are particularly concerned you can always boil it.

For anyone else wondering about "fake" table syrup:

fake maple syrup resists molds through the miracle of chemical preservatives (usually sodium benzoate and sorbic acid)

Will be perfectly fine.

Maple syrup does not have enough sugar to prevent mold and no preservatives, so like bread or wine, it can develop mold after 7 days or so, pending the environment.

1 or 2 days, not an issue.

Typically it's what you add to syrup that causes the mold after opening.

Plastic containers shorten shelf life Conisderably to about 1 month, glass and tin can do 1 year in your cupboard as long as no organic material is ever introduced into the container.