The following are the major factors that universally affect an application of a drying oil not 'drying' properly:
- Too much oil.
Not too much being applied, too much left on the surface. It's common practice to flood the wood, sort of spreading a puddle around, sometimes leave oil sitting on the surface for perhaps half an hour, and then wipe away excess1. While I don't apply oil this way myself2 this amount of oil being applied is not a problem. It's the wiping away of excess that many fall down on. My mantra is that the wood should feel dry when you're done3.
- Damp conditions, especially if coupled with lower temps.
High humidity is the bane of oil finishes and always slows down drying and curing. And if it's particularly cold it can actually prevent proper curing of tung oil and other drying oils (and all finishes made from them which includes oil-based poly, "Danish oil" and similar blended products, and the majority of wiping varnishes).
- Not enough air.
Good airflow is vital to getting oils to dry as fast as they're supposed to, just a window cracked open can make a noticeable difference but if necessary a fan set up to blow air over the piece can be necessary4. BTW this is one reason that oil-based finishes were rarely used on the interiors of furniture pieces, because the oils could take an indefinitely long time to dry due to restricted access to air.
So bearing these in mind we easily see the key elements of proper oiling technique, to prevent a sticky/gummy surface, are to be careful to wipe away all excess, if possible not to use the finish if it's too damp and cold and to ensure free access to air.
Also as mentioned in a Comment above, oils like tung are a natural product and as such can, and do, vary from batch to batch (the colour differences alone can show us this clearly). So when using a pure oil in wood finishing the oil itself can vary more than one might expect. More than it should in an ideal world but they get what they get. Pure oils can't benefit from a little additional metallic driers being added to even out drying times the way that different batches of linseed oil can when they're making BLO. This is why BLO is as a rule more consistent in performance than raw linseed, tung or walnut oils, although it too can vary in colour.
1 Coming back periodically if needed to wipe away any more that has exuded from the wood and beaded on the surface. This is reasonably common with oak for example but can be seen in other species (usually at a smaller scale though because the pores as smaller).
2 It's too wasteful and there's absolutely no difference in effect to applying the oil more sparingly at each coat and rubbing it in well — everyone using oil should do a few comparisons for themselves to confirm, to help reduce waste of expensive oil finishes.
3 Not even remotely oily. If it feels oily (and not sort of smooth and waxy) there's oil still on the surface that needs to be removed.
4 Some might worry that this will lead to too many dust nibs but that's not a concern, remember you left the surface dry after application. You did, right?