It kind of depends on where you are traveling as to how fast the tickets sell out. Last year I traveled in November (10th & 15th) using Dauer-Spezial (now SparPreis) tickets purchased on the 26th of Sept (less than 1½ mo earlier). For Cochem to Hannover via Koeln I got my choice of trains at €29. For Northeim to Karlsruhe via Frankfurt, I got about the time I wanted but had to take a slightly slower IC in order to get the €29 fare. The lowest fare was sold out for the ICE at about the same time; the next level fare, €39, for that train was still available.
OTOH, I just looked at Bacharach to Berlin for a day in March and there were no more of the lowest fares available. The best I could find was €69 for an ICE.
For April 19 (92 days out) there are still some €29 fares available, but maybe not for the time you want. There are also €39 fares available.
From 8:30 to 11:30 there are 12 connections listed, taking from 5½ to almost 8 hours. Three have €29 fares; five have €39 fares.