There are a variety of reasons why someone would decline a peerage. One of the best known is from Winston Churchill; he was offered a dukedom but declined it so that he could remain a member of the house of commons (had he accepted it, he'd join the House of Lords). Sometimes peerages are refused because the recipient is hoping for a higher, more prestigious peerage. Roald Dahl refused an OBE because he wanted to be made a KBE or a GBE, which would make him a knight. Many more peerages have been refused by people who do not view the monarchy as just or fair, and do not want to be apart of it. Others still have refused it for economic reasons as well. Prince Louis of Battenburg is the best example of this - his investments in Russia were ceased and his holdings in Germany became valueless at the end of WWI, so he refused a dukedom (though he did later accept a lower peerage).

Basically there are lot of reasons - some of them are financial, some are political, and some are for personal reasons.

edit: Prince Louis' refusal was because he felt he could not live up to the expectations of a duke with so little money, not because there are financial requirements to be a duke.

I am not a historian but I may be able to offer a little insight. The reasons why someone may turn down a Peerage or a higher office are many. It could be for financial reasons as a person of a certain station was expected to live (and spend) in a commiserate style. This would include charity, hosting and attending functions and contributing locally. Other reasons may be from a sense of honour or duty as the person may not feel worthy of the tittle that was being offered. This could come internally or from what the establishment thought of them.

An example of someone that may have elements of all of the above is Henry Addington. He was made a Viscount and then later declined the higher rank of Earl.

Henry Addington was born as a member of the gentry, became an MP in the House of Commons and held a variety of offices including Speaker of the House and Prime Minister of Great Britain. Later he was made the 1st Viscount of Sidmouth and then offered an Earldom (by King George III) which he declined. It is hard to say why exactly he declined although reputably he did so because he was unable to maintain the expenses that such an office would incur. He was a personal friend of King Geroge III and had been granted favours and pensions previously that he was heavily critised for in publications of the day. However Addington was noted for his integrity and character and it is possible that he felt that he didn't "deserve" the further title as well of being afraid of what the establishment would say. He was already mocked as the "Doctor" (His father was a famous establishment doctor and noted as having treated King George III's madness).

Sources: The Addington Family Annuals

Pellew; The life of Henry Addington

Hibert; George III A personal History

Some more information in the following links (they don't discuss Addington's decline of the Earldom): http://www.nndb.com/people/367/000102061/

http://www.britannica.com/EBchecked/topic/543103/Henry-Addington-1st-Viscount-Sidmouth

http://en.wikipedia.org/wiki/Henry_Addington,_1st_Viscount_Sidmouth