You need to first of all clear the DHCP table in the AE.. so a simple reboot might be enough.. but if not you are going to need to do at least a soft reset.
You must make sure nothing else has the IP you want to allocate.. clearly it won't work if already in the table.
You must reboot everything at times.. so the computer / device actually gets the IP requested.
So once you do the settings.. restart the whole network in correct order.. ie modem.. AE.. client.. with a few min gap to let things settle down.
Is 10.0.1.253 available in the DHCP pool.. by default apple set to the pool 2-200 so is the IP set statically??
Finally a little trick.
Set the device a static IP of 10.0.1.44.. then assign it by dhcp reservation.. then set the computer / device back to dhcp and it should then stick to 10.0.1.44
It just is a way to make sure the ARP table and the DHCP table work for you.
One PS sub trick.
If this is a Mac computer.. you can do the dhcp reservation by command line.
Use natutil command.
Terminal command to check Apple router status. natutil
natutil -L will set the current DHCP lease to permanent.
Then use the edit function from airport utility to edit the value to 44. Reboot the airport and the computer. It should follow.
Here is one I prepared beforehand.
I ran the natutil -L from the command line.
The computer was configured to the current dhcp lease in dhcp reservations.
Then I get in and edit it.
Note the utility sets the Description so that is not my doing. I would probably fix that to the actual computer name.