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Training to avoid crowding of stems will aid in the formation of flower shoots. Branches can be cut back in the spring to encourage flowering.
Best flowering is achieved in full sun.
Water regularly to occasionally when actively growing in the warmer months for best results .

Thrips can be the cause of flowers just dropping form a plant. They can be difficult to see in some cases.
You can use Neem Oil if you suspect that pests are the cause.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

This is the most common issue for this time of year. It is a fungal infection that can be cured with dolomitic lime and wettable sulfur. The old growth will not return to normal, but it will stop the spread and the new growth will be unaffected.

It sounds like the soil may have contracted an infection. Fungal/bacterial infections can come out of nowhere, but are usually the result of staying too wet for too long.

From here, you will want to treat with a fungicide. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

You may, also, want to use a handful of DOLOMITIC LIME per plant, and a teaspoon of WETTABLE SULFUR per plant. Cast this into the soil, and it will work itself in with a few waterings. This will help to take out any remaining infection, as well as condition the soil.

This article will help you with Crossvine Care: https://www.gardeningknowhow.com/ornamental/vines/crossvine/bignonia-crossvine-care.htm

Are you by any chance pruning in the fall or late winter? If so, you may be cutting off the buds that formed on "old wood." I found some conflicting information on whether it blooms on old or new wood, but generally, spring flowering shrubs bloom on old wood so you might try only pruning in late spring.

Do you have it in a sunny location? Crossvine prefers sun to bloom well. It can tolerate part shade but blooming may diminish.

It also likes acidic, well-draining soil. You can cut back on the frequent watering and go instead to less frequent, but deep watering.

Check all these variables and see if the plant is getting what it needs. Here is more:

https://aggie-horticulture.tamu.edu/newsletters/hortupdate/2009/may09/Crossvine.html

Crossvine only needs occasional pruning if it is getting out of bounds. It does bloom on "old wood" which means the flowers develop on the previous season's growth, usually the previous summer. So any pruning done in late summer or fall most likely will cut off the developing blooms. If you look closely at the vine, you will see the buds.

So don't worry about pruning the vines now, you will have another chance next spring after it blooms.

https://www.gardeningknowhow.com/ornamental/vines/crossvine/bignonia-crossvine-care.htm

This might happen with aggressive overtaking, but this would have to had covered the plant and surrounded it, preventing it from light and moisture.Typically, with regular pruning, it will not overtake anything.

However, if it was REALLY nearby- it may have choked the roots out with its own.

Here is some more information on the crossvine:

https://www.gardeningknowhow.com/ornamental/vines/crossvine/bignonia-crossvine-care.htm