Generally speaking - not my bank or any banks policy specifically - here's what might help answer your question.
1) 0-$417k Standard Conforming requires 2 months reserves
2) $417,001 to $625,500 Jumbo Conforming requires 2 months reserves
3) $417,001 to $1,000,000 Bank Jumbo requires 6 to 12 months reserves. If your loan is $550k and pricing is better than Jumbo Conforming, when using a Bank Jumbo product you may need 6 to 12 months of reserves. If you don't have it, then your loan reverts to Jumbo Conforming and the rates aren't so hot, but your reserves are OK.
In any case, some funding sources will have overlays to FNMA/FHLCM Standard and Jumbo Conforming cash reserve rules. It's rare, but it can happen.
Some lenders allow gifts for reserves. Other lenders require the funds to be cash in hand, not 401k or IRA funds. If you've got 401k assets, remember that it's 60% of the VESTED amount, not the total.
My 02c