Train Transfer Time.

8 minutes is usually more than enough, but could possibly be cutting it close if the platforms are on the opposite sides of Frankfurt's rather large station. But the onward trip to Mainz is probably on a regional train, so no problem taking the next one. At most, you'll probably only have to wait a half hour or so.

It somewhat depends on what kind of a ticket you have. If it is a standard, full fare ticket, it's valid on any train within the period of validity of the ticket. There are several S-Bahn per hour between Frankfurt Hbf and Mainz Hbf, plus other regional and express trains.

If you have an advance purchase, discounted ticket it will be more problematic. Is that what you have? If you miss the connection because the ICE is late, the Bahn will cheerfully re-ticket you on the next train to Mainz. If you miss it because you don't make good use of time, you might have more of a problem.

But, at worst, the fare for a regional train or S-Bahn from Frankfurt Hbf to Mainz Hbf is only 8,10€.

Looking at the Bahn schedule website, I see an ICE arriving at Frankfurt Hbf at 15:36, with 8 minutes to connect to an IC to Mainz. Are those your trains? The ICE comes in on track 4, the IC leaves on track 18, which is a bit of a trek from track 4. Be at the end of the coach, at the stairs, hopefully at a coach near the front of the train, when it stops in the station. Get off, go to the connecting platform, and go directly in the direction of increasing track numbers.

My first thought was that you can connect on any regional train for free, but that may not be the case. Lee, can you clarify the before-and-after regional train principle? After talking to a rep at the Reisezentrum in Berlin, she indicated that any deviation from the printed ticket would be considered a change in the trip and subject to a supplement.
In Den's case, it would seem that if he purchased a ticket with the Frankfurt-Mainz leg on a regional train, then he could use any regional train that day. But because the Frankfurt-Mainz leg is an IC train, he must use that specific train except in the case of a delay caused by DB. Like you say, continuing on the S-Bahn would not be a budget buster.

The before and after (vor- und nachlauf) principle for a Sparpreis (or, in this case, Europa Spezial) ticket just says that if your ticket includes segments by regional trains, you can use any regional train(s) on the same route from midnight (AM) of the first day until 10 AM the following day. It's printed right on the pdf file printout where the trains are specified. Only the trains of the Bahn (ICE/IC/EC) must be used as specified.

I have an old advance purchase, home printed ticket. In a box near the top labeled Gültigkeit (Validity) it says, "DB: Gilt nur in gebuchten Zügen an angegebenen Reisetagen. Im NV(S/RB/RE/IRE) auf eingetr. Strecke vor/nach den geb. Zügen am 1.Tag u. Folgetag bis 10 Uhr."

DB: Valid only in booked trains on specified travel days. In local trains (S/RB/RE/IRE) on registered route before/after the booked trains on the first day and following day until 10 o'clock.

In Den's case, I don't think he's already bought his ticket, but the connection he was looking at included an IC from Frankfurt Hbf to Mainz Hbf, so he might not be able to substitute a regional train or S-Bahn. If he hasn't already purchased a ticket, he needs to use the "stopover" function to specify Frankfurt Hbf as a place to change trains. Then he goes to "change other data" -> "Advance selection of means of transport" and unchecks the first three boxes (to the left of NV=Nahverkehr, local trains). Then he will get a ticket with Frankfurt to Mainz via S-Bahn and he can use any S-Bahn. It will take a little longer this way, but there would be no concern over making the connection.

However, I believe that if he has a Standard (full fare) ticket, it's just a ticket to get from point A to point B on a specified route. He could use any train of the same or lower class to get to his destination. He just couldn't book an IC and get on an ICE or take a route that goes through Hamburg.

I once advised someone who was planning to go from Amsterdam to Koblenz. They wanted to stop in Köln to look around, but they didn't know for how long. DB was giving them a connection by ICE from Amsterdam to Köln and by IC from Köln to Koblenz. They could specify a stopover in Köln of two or four hours, but they would have to be on the specified IC to Koblenz. They could not stay longer in Köln or leave earlier. I suggested they use means of transport to specify a regional train (RE pr RB) to Koblenz, then according to the Vor- u. Nachlauf principle, they could stay as long as they wanted (up until the next morning). I called DB and verified that they could do this.