could you amortize it as a start-up cost for your rental business?
No. When it comes to rental property, amortized costs are those costs associated with acquisition of the loan, if there's a mortgage on the property. Whereas those costs associated with acquisition of the property are capitalized. Since you already own the property, and repairs have nothing what-so-ever to do with acquiring the loan/mortgage you may have on that property, you can't claim it.
Note also that in the IRS publications (namely Pub 527) there are no start-up costs associated with rental property mentioned anywhere in that pub. I've also never seen it in any other pub related to rental real estate property.
