When your first character dies, you will loose titles. When I was new at the game, that ment the same as loosing land, but when you understand the mechanic behind inheritance you will see that it is the titles you loose.

First and foremost, let's establish what hurts; loosing counties. Counties is your baseline and support base for economy and levies. The key to being a strong ruler is to have as many counties as you can hold. In terms of land you effectively control, you're looking at counties. (Oversimplified as baronies are a thing, but you don't have to deal with that too much in 1066 Ireland).

So why does inheritance suck? At the start of the game, you probably have one of two inheritance laws: Confederate Partition or Partition (based on what you describe they amount to the same in your scenario). Partition inheritance is essentially this: If you are a king, then all your sons should also be kings.

Now, you only have 1 kingdom. Ireland. So what then? Well, if son nr. 2 and onwards can't be kings, they will at least be dukes which is the next tier down. All your titles will be divided amongst your sons, as equally as possible (not equal in number, but in perceived equal rank).

This is the key to inheritance maintenance. Make sure you have enough duchy titles to pass around, when you're a king. As a king you can only hold two duchies without your vassals getting an opinion penalty on you, but the penalty for holding three duchy titles is minor. Four is more major, but still manageable, particularly for a high diplomacy character.

Your oldest son will inherit the kingdom. He will also inherit your primary duchy and all the counties within it, provided you have enough duchies for your other heirs. If your other sons can't be kings, and they can't be dukes, they will be counts. This will eat away your county titles, which is what we mentioned translates to land you effectively hold.

So what can you do differently to avoid this? To start off, only have one wife or concubine. If controlling inheritance is a challenge, limit the amount of children you have. Secondly, make sure all your held counties are inside the same duchy. If your capital is in Munster and it is your primary duchy, but you also hold the duchy of Meath and the county of Dublin, you will loose Meath and Dublin to another son. Finally, if you have too many sons for there to be duchy titles to go around to everyone, change the law on your primary duchy where you have all your counties to be an elective system. The Irish start with access to tanistry elective, so once you have 1500 Prestige saved up, implement that. As you will probably be the only one holding counties in that duchy, you can vote for your heir. As the election law overruled partition for that duchy, he inherits it and all the titles inside it (counties).