It seems to have been implied that using the Repository of Knowledge could force someone to ascend, should their brain be unable to withstand the strain. However, since Daniel has ascend multiple times already, why has be not tried to use the Repository, if only to keep Jack from having to keep having his mind Roto-Rootered?
It is very unclear if Daniel had the ATA gene - naturally, through gene therapy or former ascension - or if his prior ascesion allowed him to circumvent the need for said gene:
Like Anubis, Dr. Daniel Jackson may possess some variant of the gene given his Ascension, but he was never seen using Ancient technology save for when he used Merlin's Repository of Knowledge, which may have been programmed to allow for less restricted access, and was once even attacked by an Ancient defence system that apparently attacked those without the gene (Although it may have been that the system simply didn't recognise him as an Ancient but would still have allowed him to control technology). When he and Dr. Rodney McKay was abducted by the Vanir during their attempt to activate the Attero device, the Vanir only used McKay to activate the technology, but this could have been because of McKay's superior scientific knowledge rather than because Jackson lacked the Ancient gene; any references to McKay alone possessing the gene could be taken as an ignorant assumption rather than a proven fact. (SG1: "The Cost of Honor", "The Quest, Part 2", "The Shroud", SGA: "First Contact", "The Lost Tribe")
Lost in translation
But even if he did have it, there is the issue Revenant pointed out: Sooner or later you need someone to translate for whoever has used the repository. And Daniel was the only one speaking ancient in any relevant way at the time.
No save way to keep it
As for using it safely? I doubt it. The issue is that the information in the repository, the transformation started by the Ancient Ascension Machine or transfering the mind of Merlin is invariably too much information for any organic mind. Sooner or later your nervous system has to drop important processes like "breathing".
It is quite possible that the rule about "you do not keep ascended knowledge" is there for the persons protection too. When descending, Orlin was unable to keep his knowledge for long - despite trying to extend the amount by reincarnating as a child.
Ancients are more then the ATA gene
The ancients themself might have been able to savely go to near-ascension, at least for a while. But they had a few millions years of evolution and genetic engineering on top of the ATA gene. The ATA gene was more like a biometric lock.
Daniel does not have the Ancient Technology Activation gene. Thus he cannot use the advanced systems such as the repository of knowledge nor the control chair, puddle jumper, nor Attero device.
It's possible that through his Ascension or McKay's gene therapy he could have acquired it, but he is never seen using any technology that requires the ATA gene, so we can probably assume he didn't.
Could Daniel Jackson have safely used the Ancient's Repository of Knowledge?
Well, it depends. When are you talking about? If you're specifically thinking of after his "descent" back into the mortal realm, probably not, although there is no reference in the series or movies that provides a good reason beyond what was already established for Jack. Others have mentioned that Daniel probably didn't have the ATA gene, but I counter that with the fact that the 1st Repository reacted to Teal'c who most definitely didn't have the ATA gene, either.
But...to take them in order: The first time (when Jack used the knowledge to dial up Asgard): probably could have used it, just not safely. Probably would have had the same outcome as it did for Jack. If you notice, the "translation" services provided by Daniel don't really change Jack's behavior in any meaningful way, except to allow the team to come with him. Sam could have techno-babbled a translation matrix to accomplish the same thing while Daniel was still coherent.
The second time: same thing, again, as Daniel still hadn't ascended.
The third time: this was Merlin's consciousness, not the full repository of Ancient Knowledge. The episode clearly indicates that it is a subset of the Full Repository and therefore should take longer to completely over-right an individual's consciousness. Merlin clearly had no issues with it, as he was an Ancient, and it was his repository. When Merlin's mind merged with Daniel's, it still had the power to control the amount of information being "unspooled", but even that had it's limits and essentially provided a "count-down" timer to when Merlin would have to leave Daniel and take the knowledge with him, thus effectuating the same kind of rescue that the Asgard provided Jack with the 1st Repository. Not exactly safe, but not highly dangerous, either.
As for why he didn't try: because sometimes knowing that you don't know if all that you need to know. Pre-Ascension Daniel saw the damage it did to Jack and the reasoning of being a translator for him was good enough. Post-Ascension Daniel, well...it could be any number of reasons, from fearing a reprisal by the Ascended to fearing remembering what he knew when he was Ascended only to lose it all again, feeling safe in knowing that he once knew and would probably know again, feeling safe in the idea that the knowledge was too much for humanity to have all at once (see also the Harcessus [sp?] episode), being accepting of the notion that sacrificing oneself (or appearing to) was something that meant more to Jack than it did to him. There is no prime canon explanation. Beta canon may have something, but I avoid beta canon like the plague, so...there ya go