TLDR: The main reason for this indirectly stems from the War of the First Coalition - after the battle of Valmy (and the subsequent development in the war) the Habsburgs were weakened and had little choice but to accept the further partition of Poland by Russia and Prussia as a reality. There is also the matter that the Habsburgs did not wish more land in Poland, particulary they did not want a common border with Russia and preferred having a buffer state between them. Ultimately this was a big diplomatic defeat for the Habsburg Monarchy.

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After the arrest of Louis XVI and Marie Antoinette during their botched flight to Varennes in June 1791, the relationship between revolutionary France and the Habsburg Monarchy started rapidly deteriorating and the latter felt that war was imminent.

Moreover the Habsburgs felt increasingly isolated in the Polish question as they opposed a further partitions of Poland and supported the Polish constitution from May 1791 which the other two powers did not. Catherine the Great flatout considered invading Poland which she ultimately did in the support of the anti-constitution Targowica confederation and defeated the pro-constitution forces.

The Habsburgs thus wanted allies against the French and escape the potential isolation in Poland, so they looked to Prussia.

Frederick William II, the king of Prussia at that time, had his eyes on Poland at the moment and while he disliked the French revolutionaries, he was willing to ally with the Habsburgs only for a proper 'compensation'. The Habsburgs were under severe time pressure as the war with France could erupt at any time and so Emperor Leopold II agreed to a some sort of a compensation in favour of Prussia, however this compensation was not specified as Leopold was unwilling to promise anything concrete, and signed a treaty of alliance against France on 7th February 1792.

On 1st March 1792, Leopold dies and Francis II takes the throne. He was willing to promise the Prussians certain concrete concessions in Poland in exchange for their consent for a swap of the Habsburg holdings in Netherlands (the so-called 'Austrian Netherlands') for Bavaria^1.

During these negotiations however France declared war on the Habsburgs on 20th April and Prussia honored the treaty from February. The negotiations between the Hohenzollerns and the Habsburgs continued, the Polish-Bavarian plan was accepted in principle in July, however the Habsburgs wanted to make the exchange immediatelly and wanted some additional territories (eg. Ansbach) to which the Prussians were unwilling to give their consent and the negotiations stalled.

In September, the coalition forces were beaten by the French at Valmy, which caused the Prussian army to retreat to the east of Rhine with Frederick William sending a de facto ultimatum stating that they need to acquire an immediate compensation in Poland otherwise they would not re-enter the war with France. Meanwhile, the Habsburg forces suffered further defeats and the entire Austrian Netherlands were occupied by the French which made the Polish-Bavarian plan de facto impossible.

The Habsburgs were intially reluctant, even threating to share their letters with Britain (as Britain opposed the partitions), however they ultimately accepted the demands seeing that after the defeats they suffered in the Austrian Netherlands they had little choice but to accept.

Meanwhile Catherine II, after changing her opinion on the matter several times, decided that it would be best for Russia to partition Poland yet again against the wishes of the Targowica Confederation with whom she allied in the war against the pro-Constution forces, and sent envoys to both the Prussians and the Habsburgs, wanting to do another 1772-style partition.

However the Habsburgs were reluctant to commit to this and after consultations with the Prussians, Catherine decided to simply cut the Habsburgs out as they could potentially cause problems - the Habsburgs neither wished to have a common border with Russia, which could lead to more conflicts, nor a substantial increase of territory ruled by the Prussians - and were weakened by their war with France. The only thing that they were willing to give to the Habsburgs was a rather vague consent for the Bavarian-Netherlands swap that however was at that time only a rather distant possibility and ultimately never materialised.

^1 The idea of swapping Austrian Netherlands for Bavaria was not new, it first apperead after the War of Spanish Succession and later during the War of the Bavarian succession in late 1770's.

Source:

LUKOWSKI, Jerzy: The Partitions of Poland 1772, 1793, 1795, 2014