How long can a house remain in my fathers estate after death.

There is no hard and fast deadline for this: a house may remain in an estate until probate is done, and sometimes--e.g. if there are complicted financial or tax issues, a cloud on title, or a dispute between heirs, such as over a will--that can take many years.
However, an executor has a "fiduciary duty" to the heirs and beneficiaries (e.g. to the other heirs and beneficiaries, if he is one of them) to act fairly and in their interest, to not engage in "self dealing" or benefitting himself at the beneficiaries' expense, and to carry out the provisions/instructions of the will at the earliest reasonable opportunity. So if there are no complications here, there is no reason probate should not be wrapped up (e.g. my father's estate, when there was only 1 heir and no issues, was probated start to finish in 6 months). If you believe, as is not unlkely, that your brother is deliberately not finishing probate so he can keep living in the house while having the estate pay taxes for him, you can bring a kind of legal action traditionally called an action for an "accounting" to make your brother "account for" his actions as executor. A court can order him to finish probate and/or sell the house so as to distribute the proceeds, and could order him to personally repay funds to the estate which he used to benefit himself (e.g. amounts paid for taxes while he lived in the home for an unnecessarily long time). This kind of action can be procedurally complex; if you wish to look into it, consult with a probate attorney.