I could not find any thread regarding this but was wondering if anyone ever had a similar experience. First, I understand that fares are kind of dynamic and may change all the time but no to that degree.

I had a reservation for my inbound flight PHL-ZRH and wanted to change it to PHX-PHL-ZRH. I saw that a one-way fare for PHX-PHL is $400.
I reached out to reservations via Twitter and I got this response:
When I got this response I thought I'd never pay $1400. So I was actually considering to just buy that one way ticket for $400. Just before I did that (and this is a few hours later). I took another attempt but this time via chat and they were able to make the change with a fare difference of $62.

What are the odds of the fares being that dynamic? Or is it just a handling mistake by an agent? It's actually not the first time that has happened to me.

I think it's just very dynamic, last Wednesday I needed a same day ticket MIA-TPA, saw it online for $1,200 but couldn't book it using credits. Called and had the agent price the ticket and it came back at $900. Was surprised that such a last minute booking fluctuated so much in 5 minutes and for my benefit.

It is probably down to availability in booking classes.

e.g. the lowest booking class for one way PHX-PHL is V class - the lowest booking class for ZRH-PHL is different with V class ZRH-PHX being about $750 more than cheapest fare

Making a change for PHX-ZRH would be based on fare on best availability for PHX-PHL-ZRH

The 1st agent may have made a mistake or it could be that there was , say, a cancellation of a hold or booking and availability opened in a cheaper booking class for PHX-PHL-ZRH

I'd check what was actually ticketed. This seems like a wild swing that I'd double if not triple check that what is now ticketed is what you want.

On Expertflyer it showed 7 in all economy booking classes except Q and O showed 0.
Usually, I am use to chat agents making mistakes, not the twitter ones.

Ticketed in the sense of the booking class or just the flights?

Did you check individual flight bucket availability or married segment availability? Adding segment will change the fare from a PHL-ZRH fare to a PHX-ZRH fare (fares are not priced hop-by-hop). There are other things that can come into play here like advance purchase requirements (just because there is bucket availability in lower fare classes doesn't mean there are cheaper fares that can be purchased in those classes due advance purchase requirements for them). Without further info on dates of flights, etc., there's not much to go on here.

What do you mean by, "that dynamic"? You only described one change. Prices can change daily, or even more often, and fare buckets sell out and become available Everttime a price changes there is a good chance that someone is a witness to the change (i.e. they saw the proce before and after the change).

The issue is that you are changing your routing. It requires a re fare on this return portion. Just buy the $400 ow.

Why? later on when the OP called again, there was avalability at a fare difference of $62.

A few months ago, I had a similar issue where the add/collect was materially different within a few minutes. As it turns out, the system bumped me out of first class on a segment that wasn't being changed. The web site had showed no indication that this was happening as it only showed the segments being changed. Had I not gone back in to verify the reservation, I'd likely not have noticed for several weeks. I called right away and, after an hour on the phone, AA was able to rebuild the reservation back to what it should have been. I'm not saying this is what happened here or that anything actually went wrong -- just recommending you double check the classes of service, dates of travel, etc.

I checked and the new ticket looks good to me now.

I totally understand that but based on that route, the fare that I originally paid, the fare difference didn't make any sense ($62 compared to $1400) . Especially because a one way fare PHX-PHL-ZRH on a new ticket would have been cheaper (and they are usually way more expensive than a round trip on transatlantic flights) .

Pretty reasonable odds for either.

While I understand that airfares are not priced hop-by-hop, assuming the OP are not making any change to the PHL-ZRH that are already booked, couldn't the PHX-PHL segment be added to the ticket as an additional "bound" and make the reservation a multi-city booking?

Alternatively, my understand is that the agent can also book a separate/additional ticket for the $400 PHX-PHL under the same PNR and not change the original ticket.