Jeff Stelling wrote:

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perhaps one of them sparked the other out during an argument

perhaps there is nothing controversial at all and they feel the relationship is stale and has run its course

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 This.

Spectator wrote:

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Well, yes. This is a bit of a surprise. But there are so many possible reasons. Indeed, while it may sound mundane, the fact that Australia is about as far away as you can get from the UK could be one ....it basically means that if you're training together in the off-season, someone (or both parties) will have to give up being at home. Brazil isn't nearby, but it's closer, and if I remember correctly, Mr Murray's wife is Colombian. Who knows! At any rate, I hope they do go out with a brilliant showing as a partnership - and that the partnership with Soares works out well, too. He's a fun player to watch.

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There's a more detailed article by Barry Flatman in today's Times which would suggest that it was Jamie who called time on the partnership ("Murray drops partner as grand-slam final defeats take toll").  Some selected paragraphs:

Jamie Murray, twice a grand-slam doubles finalist this year with John Peers, has decided to break up his partnership with the Australian just as the pair stand on the verge of qualifying for the Barclays ATP World Tour Finals for the first time.

Murray and Peers, who are fourth in the Race to London rankings, will remain together until the end of the year and are competing at the Erste Bank Open in Vienna.  Today they will play against Alexander Peya and Bruno Soares, the 33-year-old who will be Murray's partner from the beginning of next season.

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Signs of a potential split between Murray and Peers appeared last month when the 29-year-old Scot opted against playing the Asian swing of tournaments in Bangkok, Beijing and the Shanghai Rolex Masters, where sufficient points were on offer to guarantee their place among the world's top eight at The O2.

Murray said that he was feeling weary and needed a few weeks away from the Tour to revitalise himself before forming part of Great Britain's Davis Cup team fro their final against Belgium from November 27 to 29.

However, the harmony between the pair is not as strong as it once was after demoralising defeats in the Wimbledon and US Open finals.  Unbiased observers came to the conclusion that Peers, the 27-year-old right-hander from Melbourne, was the weaker link when the pressure mounted.

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Murray's decision will be seen as something of a gamble.  He ended his other long-term doubles relationship with Eric Butorac, the American, and grew to regret the decision as he struggled alongside May Mirnyi, of Belarus, a more prominent competitor.

Murray has been on amicable terms with Soares for several years.  The right-hander from Belo Horizonte speaks fluent English and is a respected member of the ATP's player council. [...]

My bold - highlighted because a similar comment has already been made on here.

Jamie will now face another former playing partner in the semi:

SF:  Fabio Fognini & Max Mirnyi (ITA/BLR) CR 42 (11+31) vs (2) Jamie Murray & John Peers (AUS) CR 15 (8+7)