When your ISP's DHCP servers give you an IP address, it's leasing it to you, usually 24-hours to 5-days, depending on the provider. If you set your adapter settings to use an IP address, it does not make it static. All its doing is forcing the adapter to use an IP address your ISP's DHCP servers have already leased to you. If you lose that lease, it will let you use the IP address until the user in their system who it's leased to comes online - then it will boot you off and assign the IP address to them.
Don't be fooled by this because it works when you try it. It doesn't mean anything except that the servers already leased the IP to you so it's letting you use it. If anything it will create a less stable situation where you will eventually lose the lease and then the IP address you're using for your MC server will no longer operate while people are either connected or trying to connect.
The best way to keep an IP address that is not static or reserved by your ISP is to not lose to the lease. You can do this in different ways, but first you will IPCONFIG /ALL and determine the Lease Obtained.
For example, mine currently is leased from my router: Lease Obtained. . . . . . . . . . : Sunday, April 5, 2015 6:06:50 PM
Once you have YOUR least obtained time, you look at the line Lease Expires.
For example, mine is: Lease Expires . . . . . . . . . . : Wednesday, April 8, 2015 6:06:58 PM
You can see the difference in timeframes. I have configured my router to provide a lease for 48-hours before releasing the IP address assigned back into the IP pool. The reason for this is, I have many computer systems in the home at any given time for repair and thus want those machines to keep the IP address they were assigned while I am working on them, but later it does not matter, so it can release the IP. This is for my local network, not the ISP. However, if you're using a router, just ensure it's always connected and operational and it should be able to keep your IP lease virtually forever.
If I look at my router, which is connected to the service provider, it tells me:
Lease time
1 days
Lease expires
18 hours 58 minutes 31 seconds
It does the work for me - it already sorts out that I have an IP lease for 24-hours (1-day) and expires in 19 hours basically. If you are directly connected to your Internet, you will use the IPCONFIG /ALL to determine the lease times where I am just using my router to tell me information.
What does this mean? Well, it means if I am not actively connected to the ISP when that lease expires, and a new user on their system connects their internet and is leased out an IP address, they can be leased the IP address that I had. If they don't before I reconnect, the DHCP server will oftentimes give back the IP address even though it's no longer leased to me.
Now, I've used mine as an example. In reality, my router gets a reserved IP (works like a static IP address but their DHCP server assigns it only to me and never anyone else and I don't have to set up the static assignment - it's automatic). It's still leased as per 24-hours because that is their DHCP lease time system wide.
Most people do not have a static or reserved IP address. To keep yours, use a router (which most people do) to hold onto the IP as if it's on and connected to the ISP, the lease will just renew the same IP address you're already connected to.
What if you don't use a router? If you don't use a router, then you will want to keep your computer turned on and connected to your Internet all the time. If you don't want your computer on 24-hours a day (including hibernation as it can lose its IP address if it's sleeping when the lease expires) then buy a cheap router. Even if you don't really need one, it can keep your connection alive with the use of very little energy and they're not expensive to buy.
If you just want your IP address on your local network over the router to never change, then you can enter your router setup and just reserve the IP address for your network adapter. You wouldn't set it statically in Windows or other OS - you just set up the router properly.