I agree that there'd be no more development, but do you think it would be costly (or otherwise resource consuming in a meaningful way) for them to keep the static product going?
There are always costs.
Software licensing, storage, hardware refresh, systems to validate that the servers are running and the applications are responsive, operations staff to monitor, adjust, and repair the inevitable failures all come with a cost.
Is that cost high? Probably not since WotC runs a larger farm for its Magic side, but it does exist.
Likely, they'll keep running 4e DDI so long as the subscriptions are high enough to offer enough of a premium above those costs and then they'll announce a future date shut down.
If 5e flops and DDI subscriptions don't warrant keeping the whole digital initative alive then it'll get pulled faster as the whole cost is certainly much higher than the portion that would be charged to 4e life-support.