It would seem that his downfall was possibly as a result of him, whether knowingly or not, flaunting his success/blessings.
There is an interesting essay here p.16 which writes as follows:
The Death of Rabbi Acha bar Yaakov
In the following story, Rabbi Acha bar Yaakov dies from an ayin hara (evil eye). Rabbi Rosenfeld (n.d.) explains that a person should have humility and not flaunt his blessings. One who shows off draws the attention of others and incites them to jealousy. By doing this, the person may cause the Heavenly court to reconsider the good fortune bestowed on the flaunter. Several commentaries note that the sages did not intend to harm Rabbi Acha but this resulted from their surprise at his amazing achievement. In any case, the lesson to be learned from this story is to be discreet with one’s accomplishments and not boast about them. The Talmud frowned on ostentation (see Friedman, 2002).
When looking into this more deeply, a different idea emerges that it wasn't so much him flaunting his successes, but rather it was his successes that perhaps made him more bold in his actions. This resulted in him acting on a level that he was not able to do so, which brought about his untimely death.
The Chiddushei Chasam Sofer writes as follows:
רב אחא בר יעקב כ' חד וכו' ונח נפשי' אולי חשבו שע"י השבעת שם נזדמן לו כך ולא חשבוהו ראוי לשמש בשמו' ע"כ יהבו בי עיני' ונח נפשי' כדפי' הרע"ב על ודאשתמש בתגא חלף ע"ש וברמ"א י"ד סס"י רמ"ו ובש"ך שם סק"ו:
Rav Acha bar Yaakov...and he died - Perhaps they thought that through the swearing in of a name (i.e. the sheim Hashem) happened to him and he was not considered worthy to use His name. Therefore the Sages looked at him and he died - like the explanation of Rav Ovadia Bartenura on the words "One who makes [unworthy] use of the crown [of learning] shall pass away" (Pirkei Avos 1:13) over there. And in the Rema YD 246, and the Shach there in seif kattan 6.
Taking our cue from this, the Bartenura on pirkei avos writes:
"And one uses the taga (crown)": One who makes use of the crown of Torah in the way a man uses his tools, passes and leaves the world. And there are those that explain taga to be the initials of talmid gavra acharina (the student of another man), as it is forbidden to take service from students that are not his students. And I have heard, "'And one uses the taga,' meaning to say one who makes use of [God's] explicit name passes and is lost, as he does not have a share in the world to come." (Sefaria translation)
So it would seem, however we are meant to understand it, that Rav Acha whether knowingly or not, did not "use" Torah in the appropriate way and that led to his ultimate downfall.
Based on the Rema in Yoreh Deah 246 I came across the Avos D'Rebbi Nosson which ties in with the Chiddushei Chasam Sofer above:
ודאשתמש בתגא אבד ואזיל ליה כיצד שכל המשתמש בשם המפורש אין לו חלק לעולם הבא
He who uses it as a crown, perishes, and then it is lost to him. How so? For anyone who uses the Ineffable Name of God has no share in the World to Come.
So conceivably, he used the sheim Hashem but wasn't on the level to use it which possibly led to his death.
EDIT
I saw another more esoteric approach in the Chazon Ish, Choshen Mishpat - Bava Basra in the Likuttim siman 21 (see half way down the right column with the bolded word "sham") which demonstrates the power of ayin hara which does not negate Rav Acha's piety or tzidkus (and therefore preserves a good view of him unlike the first answer). In short, Hashem's hashgacha is often performed by a tool called the ayin hara which was triggered in this case causing Rav Acha to die.
He writes there:
שם יהבו ביה רבנן עינייהו ונח נפשיה
מסודות הבריאה כי האדם במחשבתו הוא מניע גורמים נסתרים בעולם המעשה ומחשבתו הקלה תוכל לשמש גורם
להרס ולחרבן של גשמים מוצקים וכדאמר פסחים דף נ' ב' כיון דנפיש אפחזייהו שלטא בהו עינא ובב"מ פ"ד א' לא מסתפי מר מעינא בישא
The Sages looked at him and he died - The secrets of creation are such that man in his mind motivates hidden factors in the world of action, and his light/simple thoughts can serve as a cause of destructive rains. Like we say in Pesachim 50b " Since their volume is great, the evil eye dominates them" (i.e. because he has such bulky merchandise it appears like he has a quite significant business which can bring an ayin hara), and in Bava Metziah 84a "Isn’t the Master worried about (being harmed by) the evil eye (by displaying yourself in this manner)?"
So the Chazon Ish explains that human thought can influence and impact on the physical world in a destructive way.
He continues that sometimes while humans admire a successful reality they actually place that reality in jeopardy.
ובשעה שבני אדם מתפעלים על מציאות מוצלחה מעמידים את מציאות זו בסכנה
As a result, the Chazon Ish reasons that הכל בידי שמים - everything is in the hands of Heaven, and anything that is not decreed with heavenly judgement to be lost/removed is accordingly saved. However, if that thing has indeed been judged to be "lost"/removed than the end result is sometimes rolled over on to an "עין תמהון" - "wondering eye(?)" and it is through this that the thing comes to an end.
He explains based on Bava Metziah 107b the overwhelming power of the evil eye and how it is responsible for death far more than normal natural death. The Gemara there reads:
The Gemara returns to expounding the themes of blessings and the evil eye. The Torah states: “And the Lord will take away from you all sickness” (Deuteronomy 7:15). In interpreting this verse, Rav says: This verse is speaking about the evil eye. The Gemara comments: Rav conforms to his line of reasoning, as Rav went to a graveyard, and did what he did, i.e., he used an incantation to find out how those buried there died, and he said: Ninety-nine of these died by the evil eye, and only one died by entirely natural means. (Sefaria translation & notation)
He explains the Gemara to mean that when they were sentenced to death on Yom Kippur, they were confronted by an evil eye and it was that "rolled" on their death.
As a result he concludes:
וכן ראב"י כשהגיע זמנו ליפטר מן העולם ונגזר עליו זמנו גלגלו מן השמים סיבת מותו ע"י הערת תמהון בלב רבנן
And similarly, with Rav Acha bar Yaakov when his time came to depart from the world and his time was decreed, the cause of his death was rolled up from heaven by a note of astonishment in the heart of Rabbanan.
So in short, I believe this is saying that Rav Acha bar Yaakov was due to die but there needed to be a reason for this death to come about and this presented itself when the Rabbonim looked on at him with wonder, which initiated some sort of ayin hara which duly triggered his death.
