Influence does not limit the number of children a house can have (otherwise House Frey would have an Influence of several hundred!) but rather how many heirs with a significant Status you have.
The problem we're having is that when you have a house with 35 Influence, invested into a first-born son (20) and a daughter (10), when the old lord dies, the house loses Influence (from the last heir in line, 10 in this case). This can mean some strange things, such as a Lord having a son, and the son assuming the head of house role when the Lord dies, but the house's Influence drops so much that the son, according to the rules on maximum status, loses his lordship and becomes a landed knight. This is absurd, surely?
Also, an example from my game, the house had a lord (NC) and two heirs, male (PC) and female (PC). The lord was killed, so the house loses Influence, and if the male heir is killed, or sent to the wall, the family dies out, because there are no male heirs, right? This means that a house can very easily be wiped out.
My solution was to say that you can have more children of the Lord, and the heir can have 2-3 children, but these do not count as "significant" heirs. So if you have a lord who dies, his only significant heir is his only son, but that son may have 2-3 children, they however are maybe infants, and there unfit to rule, and therefore they would be next in line as heirs, but they would not be significant, and therefore would have lower status.
Does this make sense? How should we deal with this?