The "Krim" refers to Crimea, so this is a tomato that originated in Ukraine, formerly part of the USSR, across the Black Sea north of Turkey. Tropical compared with more northerly regions of the USSR, but not by most standards.

When you say the blossoms are dying, I'm not sure what you mean. For instance, do you mean:

1. the flowers bloom, then the yellow petals fall? Some people worry about this, but it's normal for the petals to fall after the flower passes its prime. If the flower was successfully pollinated, a small tomato will appear after about a week. Here's a photo timetable:
http://www.tomatosite.com/index.php?NT=Cultivation&RE=Truss_Timeline

2. the flower blooms, then the flower, its green sepals, and part of the stem all fall off together? This is called "blossom drop." It means that pollination failed, usually because of temperatures which make the pollen ineffective.

It could be that the days are too hot (usually somewhere in the low-to-mid 90s), the nights are too hot (the low temperature 75 or higher), or that the nights are too cold (the low below 55). In this situation, you can try to hand-pollinate or shake the blossom during the part of the day when temperatures are more moderate.

[As for the cherries fruiting successfully in the same conditions: well, cherries are tougher than other types of tomatoes, and they are often able to fruit in unusually high heat; I don't know if they react similarly to cold conditions. I don't know how Romas react to borderline heat and cold.]

You can read more about blossom drop (including the use of hormone sprays) in this forum's FAQ, linked at the top of the forum's main page:
Why are the blooms on my tomato plant dying and falling off?

3. Or is it that the flowers are withering before they bloom? I've seen this happen when the plant is stressed -- or simply not ready to support fruit yet.

Does the BK seem at all stressed, compared to the other plants?

In addition to all the good info from missing above, BK is a late season tomato (85-90 days) so either delays blooming or often drops early blooms if the conditions are not ideal (like most late season varieties do). It cannot be compared to cherry varieties or Romas which are early to mid-season varieties.

Insure you don't have one of the contributing factors to blossom drop going (linked above) - like the night time temps, humidity,etc.)- and then be patient.

Dave

my Black Krim is doing the same thing! The blossoms just drop without any pollinating. All of my cherries, my better boy, celebrity, mariglobe, and several others all have developing fruit on them but none of the black krim. The weirdest part is that the BK plant has the most overall flowers. Last year this time the BK was packing on some serious weight with all the emerging tomatoes, but not this year. Im pretty frustrated.

I can't help but wonder that since the Black Krim is an heirloom and not a hybrid tomato, it's going to be a little more finicky when it comes to weather conditions? Heck, if I were going to "make" a new type of tomato, I'd want to engineer it to grow under less than ideal conditions.

I have to keep reminding myself that's not even June, and patience is in order.