There is now a device which one can use to store time. It is small and inconspicuous, but takes some setting up to use (explained more later). Essentially, it will temporarily remove a region of space from space-time. Once that region of space is returned (but not before), your device has stored the "time" for that amount of space. A device can only store or be activated on one region at a time, but not both.
For example, if you had removed a cube of space that contained your house while you were at work for 8 hours and then returned it when getting home, you could activate the device to gain an extra 8 hours of free time for your entire house. While within the house, the outside world would appear to be stopped.
However, those who really want to take advantage of the device could also store their whole house, and after getting home, activate it on a single room — which in this example will take up 1/10 of the previously stored area — which means they could have it for (8 hours × 10) = 80 hours!
Setting up the device requires "tracing" the area you want to remove or activate on with the device. There is a volume limit of 10 meters cubed (1000 m³).
A device itself cannot be removed from time. The device attempting to do the removing will just give an error beep and reset (meaning the area has to be retraced).
Anything except for the device itself can be removed from time. For objects being removed, time does not pass.
When returning a stored area, it must be returned to the space it was taken from. But, the stored time you get can be used on any area (after tracing).
Removed areas of space are not there. The adjacent regions of space are connected instead. This means you could remove an area 10 meters long, take a single step across where that area used to be, and restore it — and then you'd have moved an extra 10 meters. If a person were standing right on that dividing space and it was returned, they would be split in half — with 10 meters between the halves.
---{|||||||}--- If the {||} is where space is removed, it would instead look like ------
People (and other objects) still age when activating the device for "extra time". This means someone could take their baby child home, activate the device and live through 5 years (if they had that much saved up), and then emerge the next "real" day with a 5 year old.
Assume this device is somewhat expensive, but very common for first-world countries (Let's say about $500 USD in today's monetary value)
Devices do not last forever. When breaking or expiring, nothing catastrophic happens — any stored region of space is returned and, seemingly as far as we know, the time that would be stored is just lost.
With this device, as a society, some people choose to age themselves for extra spare time. Others don't. And still others have a trusted individual remove them from time so they are brought farther into the future.
Other than birthdate no longer being a reliable way to tell "age", What major difficulties would societies face because of this new invention?
Answers should be judged by the degree of difficulty the society would face and the likelihood of the challenge emerging.