Based on Erik's answer about "The Chase" I looked through the transript
In the Laboratory:
CRUSHER: The computer might be able to find that pattern.
PICARD: Doctor, programme the computer to analyse the distribution of the pieces that we have, correcting for changes in star configurations over four billion years, then extrapolate for the missing piece.
CRUSHER: That's going to take several hours to set up and to process. If you'll excuse me.
In Ten Forward:
DATA: The computer is processing the data. I will be notified as soon as there is any information.
In the Laboratory:
DATA: The computer has completed its analysis.
CRUSHER: The computer was able to extrapolate this geometric pattern based on the distribution of the fragments.
Since the computer was trying to extrapolate a pattern, it wasn't searching for data so much as going through all combinations of results. Depending on the number of variables this could explain why it took so long. It wasn't simply querying a database and taking a really long time to return the dataset.
I went through all 92 episodes that IMBD claims have the Enterprise Computer speaking in TNG. I wasn't able to find an episode in which the computer took a long time to process the information and the crew reconvened when it finished. Admittedly I was just looking for the term 'computer' in the episode breakdowns on Memory-Alpha.
There are several episodes where the computer is either disabled or behaves erratically ("A Fistful of Datas").
In "The Naked Now" it takes Riker and Data quite a long time to run down a reference to a crewman being found fully clothed in the shower. From the episode "The Naked Now" breakdown:
Riker wants some information and enlists the help of Data. He has a vague memory of reading something about a person fully clothed in a shower, relating to La Forge's find on the Tsiolkovsky. Data agrees to help Riker and commences an extensive library computer inquiry for Riker after he comments that it should be easy for Data to find the information as he is written in many bio-mechanical texts. Data is curious and inquires if he was boasting about his comment about being in many texts to Crusher. Riker comments that he possibly was in a dry way, and inquires about the time it would take for the search. It would take some time. Data, however, continues the conversation about him in texts by saying that Crusher may look him up in the texts he mentioned.
Back on the bridge, Data and Riker are continuing their search, but it is proving nearly impossible. The mention of a proverb by Riker prompts him to tell Data to search the historical records of all starships named Enterprise. As Data looks over the relevant medical records, Picard arrives on the bridge. Just as he reaches the station, Data finds the relevant information from the medical database from the old Constitution-class USS Enterprise.