ずじまい: an opportunity ending without the intended action
Describe an intention left unrealized, and distinguish it from a negative statement that leaves the opportunity open.
The situation ends without carrying out the action
手紙を書こうと思いましたが、結局書かずじまいでした。 means that the speaker intended to write a letter but ultimately never did. It looks back on an unrealized intention, rather than merely stating that no writing is happening now.
書かずじまい here also differs from starting a letter and leaving it unfinished. The focus in this example is that the intention to write did not lead to actually writing the letter.
Replace ない with ずじまい
Remove ない from 書かない to leave 書か, then add ずじまい to form 書かずじまい. 見ない becomes 見ずじまい, while する exceptionally becomes せずじまい.
行けずじまい comes from the negative potential form 行けない. 今年も行けずじまいでした means that the speaker ended up unable to go again this year, so do not reduce it to simply choosing not to go.
Compare まだ and expressions of completion
まだ手紙を書いていません。 means that the letter has not been written yet, leaving open the possibility of writing it later. 書かずじまいでした focuses on the relevant period or opportunity having ended without that action.
書いてしまいました means that the letter was written, with a possible sense of completion or regret. Despite their visual resemblance, ずじまい and てしまう must not blur an outcome without the action and an action that actually took place.
Can 今年も行けずじまいでした。 be read as being able to go but deliberately deciding not to again this year?
Show the answer and why
That conclusion is not justified. 行けず comes from 行けない and indicates inability to go; ずじまい adds that the opportunity ended that way. Deliberate refusal is not stated.