Availability is much more of an issue than any official limit. Basically, the Sparpreis offers exist in order to allow price discrimination: get people who care more about convenience than money to pay more, without losing customers that can't/won't afford the full price. So they're designed to run out well before the day the train runs and the sooner you buy, the cheaper it will be.
However, if it is an expensive ticket, there may be a semi-workaround: The cancellation fee for Sparpreis tickets is only 15 EUR before the day of the trip. So even if you're not sure about the day and time, it may still be worthwhile to buy a ticket for the most likely time (or even more than one) as soon as possible, and cancel it if your plan turns out to be different. 15 EUR is typically much less than the money you save by getting an early Sparpreis ticket.