Three from baseball:
Dropped the ball.
Meaning: A last-minute failure. See the compilation of examples and senses given at The Free Dictionary for specific uses.
He (or they) struck out swinging.
Meaning: Failed while giving it his (or their) best effort.
A swing and a miss.
Meaning: Said when the batter swings at the pitch but misses it. The effort put into the swing can be intensified by saying "he swung for the fences, but missed the ball".
Using "drop the ball", "failed to take the bow" and "overstayed the curtain call" (as well as fixing some idioms) in the examples given in the original question:
- Software was released after years of development to provide great performance and stability, but the interface developers dropped the ball | failed to take the bow | overstayed the curtain call by making the interface user-unfriendly and otherwise poorly designed.
- He wrote a brilliant essay, but dropped the ball | failed to take the bow | overstayed the curtain call by not bothering to spellcheck it, ruining all his good work.
- Bob cooked a fancy meal for his date, but dropped the ball | failed to take the bow | overstayed the curtain call by serving it on disposable plates because he was too lazy to do the dishes afterwards.
Editorializing a bit, here at EL&U three types of evidence are considered support for claims made in questions and answers. Those three types, attestation from personal experience, general reference citations, and less-general reference citations, correspond respectively to the three classes of witness noted in a common mid-1800s idiom: liars, damded liars, and experts. That idiom was later paraphrased in a related idiom concerning statistics ("there are three types of lies: lies, damn lies and statistics"), commonly attributed to Disreali--by Mark Twain, among others--but not found in Disreali's writings. The false attribution of the 'three types of lies' phrase thus testifies to the accuracy of the original concerning the classes of witnesses.
I digress to this point: a Google Ngram comparing frequency of occurrence of the phrases 'Close but no cigar', 'fell at the last hurdle', and 'stuck the landing' (an Ngram linked in the comments on another answer given for this question), as well as an Ngram comparing those phrases along with the additional phrase 'dropped the ball', are both typical examples of the second and third classes of supporting 'evidence' provided in questions and answers at EL&U.
For my part, I example the first class of supporting 'evidence' by attesting from my personal experience that not only is 'dropped the ball' a much more common idiom than other, similar sports-related idioms, it is also a much closer match in meaning to the Ukranian proverb as I understand it, than other, similar English idioms.
Having dabbled in semi-professional thespianism as a youth (viz. "1928 Daily Express 79, Oct. 9, He still wraps round him..the rags of a tattered toga of Thespianism"), my first impulse in seeking an English idiom corresponding to the Ukranian proverb concerning stage dancing was to look to the theater. British and American stage productions, after all, customarily follow the same convention that underlies the Ukranian proverb: after a successful performance, the performers are drawn back on stage by applause, where they bow to acknowledge and respect the audience's praise. This is known idiomatically in English as 'taking a bow'.
Thus, the Ukranian proverb's corresponding niche in English idiom is occupied by not one idiom, but two: the first should be an idiom expressing the extent of the effort put into a performance, the second is the mutual idiom deriving from theatrical custom, 'taking a bow'.
Because verbal prejudice denigrates what is called "mixing metaphors", and because the second idiom, common to both Ukranian and English, is drawn from stage production customs, the first idiom should also be drawn from that domain. The easy target for this requirement, and possibly also the best, would be
They danced their hearts out, but didn't take the bow.
A spin on this idea, which perhaps more closely aligns with the sense of the Ukranian proverb, draws on the custom of the 'curtain call'. Having performed and been returned to the stage by a tempest of applause, the performers are best advised to avoid staying too long, in order to not spoil or detract from the effect of the performance. So, a portmanteau idiom that expresses this idea is
They danced their hearts out, but overstayed the curtain call.
This last idiom will perhaps not be as readily or widely comprehended as the first portmanteau idiom, because 'taking a bow' is more generally understood than the idea of overstaying the 'curtain call'. Nonetheless, overstaying the curtain call after a strong or at least heartfelt performance may more closely align with the sense of the Ukranian proverb.
Just as dance, in many European countries, occupies a more prominent, more central niche in the culture than it does in America or England, so sports--another type of performance--occupies a more prominent cultural niche in America and England. Hence the almost exclusively sports-related idioms given in the answers to this question.
Nonetheless, it seems true from my experience that not only would "they danced their hearts out, but didn't take the bow" be immediately understandable to many English-speakers, it would also convey more clearly and completely the nuances of the Ukranian proverb.
In conclusion, I note that neither the translated Ukranian proverb nor the equivalent English stage portmanteau idioms I have offered will, strictly speaking, work well in the English sentence examples given in the original question. For those examples from the question, either the sports metaphor 'dropped the ball' or an abridgement of one or the other of my portmanteau idioms, that is, 'failed to take the bow' or 'overstayed the curtain call', do work well, being more compact and concise than either the Ukranian proverb or the English equivalents. Of the more concise expressions, 'overstayed the curtain call' is certain to be least widely understood.