Using TFTP to and from router

Is it absolutely necessary that if I have to use TFTP to and from another router, the host running TFTP Server program has to be physically connected to the router?
Or is there a method using which I can TFTP into a router, while the router and host running TFTP Server, is connected via a common device i.e another router

Doesn't need to be physically connected. You just need the network to have the routing in place for the router to know how to reach the TFTP server by IP address and vice versa.

So in other words, you can have several routes between the router itself and the TFTP server. If the router can ping the TFTP server, then the router can upload/download data (i.e.: config, IOS, etc) to/from the TFTP just like any other data, you just need the foundation to be in place.

Just as a note, I'd like to mention that I was faced with an extremely buggy version of the IOS (12.4.22) which didn't allow me to load a newer IOS via TFTP.

After 5-6 attempts, the TFTP session would timeout at around 95% of its transfer. Since the IOS was fairly large (~40MB), I had to start it from the beginning every time and waisted quite a bit of time.

This was the first time I encountered this issue, and was quite stunned!

I then tried using FTP instead and it worked first go! So, if anyone out there is experiencing issues with TFTP, always remember that FTP is also an option - especially if you're performing the upgrade remotely, it's recommended to make use of FTP, to ensure you don't get any problems !!

Cheers,

I had the 2600 connected to my desktop via the BT Homehub. They could ping each other both ways. But the TFTP sessions just wouldn't work. I am using Cisco TFTP application. But the moment I connected the router to the desktop directly via the crossover cable, and TFTP started to work without any issues.
I will try again later.

It still doesn't work via the BT HomeHub.
Here's the respective errors I get.
When copying files from 2600 to PC - Undefined Error
When copying files from PC to 2600 - Timed Out

Right, now solved this weirdness with TFTP as well.
Well, it was the BT Homehub. If all works well with a direct connection between Router and PC, and it doesn't if Router goes to PC via BT homehub, then blame the homehub!!!

FTP Server wasn't enabled on the homehub under Application Sharing. I had to specify to the homehub that, FTP had to be enabled to-and-from CiscoRouter2501 (which was already identified as a valid device on the network using MAC ID).
Once that was enabled, the TFTP application started to work straight away.

So, if anyone is using a ISP router e.g. a BT Homehub, or something similar, make sure FTP Server is enabled under application sharing category.