I think Dominic was saying in his own way, that how you phrased it is a little strange, but any native listener would completely understand what you meant. .. "hold down" is commonly used when speaking about employment and a job... "why can't you ever hold down a job for long":

I think "hold onto" is probably the best answer. Dominic's suggestion is also OK, but usually "putting away money" implies that you will be saving it for a long time (you "put away money" to buy a car or to pay for your kids' college education, or you "put away money" in case of an emergency). If your son's birthday is next week, it makes more sense to say you will "hold onto" (or "hang onto") some money.

I need to save some money for my son's birthday

Another possibility would be "I need to hold onto some money ..."

Hi, It does make sense but it would be more natural to say 'I need to put away some money for my sons birthday next week'. This is a more standard saying, but yours does make sense too.