What can cause tomato flowers to drop before blooming even once?
They never open at all. So, there's no chance for external pollination. They get to the point to where they're almost about to open before they fall off.
One cause: Excessive heat will do it, we had a 1 week hot spell back in July that knocked out tomato production for quite a few gardeners here.
Fortunately for my garden, we had part of the crop flower early enough and the other flower late enough that we didn't get hurt much. The ones that tried to flower during the extreme temps lost the flower buds and tried again a little too late in the season.
Diversity of varieties planted paid off really well.
More research also gives two other causes. Cool weather can cause the blossoms to drop off after they've been pollinated, and excess nitrogen can cause excessive growth with no blossoms or blossom drop.
In extreme overapplication, nitrogen can be a secondary cause of blossom end rot, the primary cause being free calcium lack in the soil.
Test the soil for NPK and acidity. For fertilizer, don't go much above 7-9-5 and fertilize after fruit has set. Burpee notes that 2-3-1 applications from time to time are necessary as Tomatoes are heavy feeders and need the nutrients. So, more light applications over time or time release will be less likely to cause issues as you're dosing nutrients out as the plant needs them.
Tomatoes need phosphorus and appropriate application of calcium in the order of Lime if the soil is too acid or Gypsum if the soil is in the proper pH range.
After testing to see if you have too much nitrogen in the soil, removing excess nitrogen involves using several methods, grow early season crops like broccoli, cabbage or other leaf vegetables that aren't harmed by excessive growth, later season heavy nitrogen feeders like corn or till in carbon rich organic materials so the soil bacteria use up the free nitrogen in digesting it.
We can get the soil right, the weather will unfortunately do what it darn well pleases.
The commonest cause for blossoms falling, particularly if they drop from the knuckle, is dryness, both at the root and in the air. Hot, dry air has already been mentioned in one of the other answers as a possible issue. Lack of pollination also causes this problem, so increase humidity and water, and if the flowers remain and do open, tap them gently occasionally to encourage pollination - this simple solution might solve the problem. If it doesn't then looking at the growing conditions (you haven't said how you're growing them, how much root room they have, etc) and then nutrient supply are next on the list, in that order. Adding extra nutrients won't be very useful if the plants don't have enough root room or aren't getting enough water, because they won't be able to take up feeds properly.