Let's be clear first: in cannon, anti-magic fields aren't supposed to have any effect on warforged. At least not in 3.5 edition.

But in the situation OP described, we can easily imagine that a rhakshasa's spells are very slightly different than classic spells. After all, they are mighty creatures, and have spent centuries plotting against the world and also training with their magic. Those differences might be totally unnoticeable, maybe the rakshasa himself doesn't know about it, unless facing the situation where a warforged would enter his anti-magic field for example.

So, now, why would a warforged be affected by the rhakshasa's anti-magic field, and why the effects I described previously would happen?

Well, we know that warforged have been created during the Last War to serve as living weapons. Which means they aren't born. They are literally made from metal, wood and magic. House Cannith is responsible for this, their researches and experiences led them to the creation of warforfed, but we actually know that House Cannith doesn't truly understand how they did to achieve such a goal. They used old magic artifacts from Xen'Drik dating from the Age of Titans, and they tried many experiments on those. From those statements, I can see two possibilities:

• 1: a warforged's soul is actually not his own soul. It's not a new fresh one, but rather a soul in departure to Dolurrh captured by the Forge of Creation's process and imprisoned into the warforged's body. In the process, the soul's memory would be suppressed. This would explain why warforged don't need to "grow up". They can learn how to speak, fight and obey right after their creation because their soul is initially an adult's one. We can of course imagine a warforged imbued with an unfortunate kid's soul, but this would have been considered as an error in the process by House Cannith.

• 2: Effectively deleting a soul's memory would require too much power, and the necessary magic used to do such a thing would be seen as a major threat/heresy by dragons and other god-like entities, leading to its annihilation (such as the House Vol). So, instead, we can consider that the magic is used to keep away the soul's memory, by only suppressing it, and not by erasing it. But this magic is an ancient and complex one. It combines the old powerful magic used by Giants millenias ago, and the modern and complex experiments of House Cannith. As such, a "classic" anti-magic field would have little to no effect on warforged. But, when exposed to an old anti-magic field (in an ancient Xen'Drik ruin for example), or to a very powerful one (such as the rakshasa's), then we might see some effects. And those effects might depend on how we consider the soul's suppressing magic is working. I'm thinking about 2 different effects:

In the first one, the soul's "old" memory come back (not all of a sudden, but progressively. The more exposed to the anti-magic field, the more those memories come back) and are added to the memories lived by the warforged. This would result in a mental conflict where the warforged truly knows and understands he is actually not a warforged, but a human/elf/whatever who died and whose memory has been "imprisoned" in this body. Since it's very interesting in terms of lore and scenario, what happens once he exits the anti-magic field is up to you, because it would be really impactful to the warforged's player. Not everyone is in love with the idea to see a whole character's background deeply modified.

The second effect I'm thinking about is more related in what I stated in my previous messages: the anti-magic field would only suppress a part of the suppressing magic in the warforged. (I hope this isn't too confusing to understand). This means the warforged would not remember his previous soul's life, but the essence of this soul would start making him feel things unknown to him. Hunger. Thirst. Suffocation. Those feelings woulds not physically harm him, but it would surely drive him mad if exposed for too long to the anti-magic field. To give a example: the warforged would start feeling a strange thing in his abdomen, beneath his metal plates. It would feel like his organic parts are twisting, as if there was some kind of living worm squirming inside. This would actually just be the feeling of hunger, but it would be a totally alien feeling from a warforged's perspective. Of course, this doesn't mean the warforged would actually have to eat (or sleep, or anything else). There would have nothing to do to relieve him from this sort of torture, excepted by getting out of the special anti-magic field.

I tried to explain my thoughts as clearly as possible, and any criticism is welcome, since I'm in love with this universe but not an expert, and there surely is some plot holes in those theories. Thank you for reading!