Let's consider warfare in its entirety.
First, not everyone will have the same amount of fame. Even common soldiers might also own lands or have fame from previous campaigns. At the bare minimum, an unknown, untested soldier will lost 8 RL days of play (4 x 2 days) for their first death. Seems like a fair exchange to spend the next 10 hours battling fearlessly. But we'll come back to that in a moment.
If you happen to be the leader of your squad, a particularly capable soldier, a veteran of past campaigns, an officer or aristocrat, or perhaps a reserve troop who's day-job is owning and managing a lot of land you will most certainly have a higher fame. That makes the first death far more costly. From 12 days at renowned ( 4(1.5x2) ) to 32 days at famous ( 4(4x2) ) . To a baron, officer or champion soldier that is a significant loss for a single death. If the less-famous troops get overrun in order to absorb the penalty early, that exposes the higher-ranked, more famous troops to a huge loss. Your officers are likely to be more conservative out of necessity.
Even so, 10 hours is a long time to wage a battle consequence free, right? But is that a long time in terms of battle length?
In medieval times, the most common type of conflict was the siege. These could drag on for months or even years. (For reference, the longest siege in human history lasted 26 years and there are many examples of sieges nearing a decade long). In Elyrian terms, that means an army could be in the field wearing down the defenses of a well-defended settlement for a month in real time easily. Your OPC will be there, night and day, week in and week out. Possibly dying several times while you are logged off.
Now consider that ten-hour window. Over a month's time with continuous battle if a common soldier took a soul penalty every 10 hours they would lose 576 days of play ( (72 x 4)(2) ). Obviously no soul can absorb such a shock. You would reach permadeath in under 20 days. And the problem only grows worse if you are successful and manage not to die, as you will certainly gain fame on the battlefield. A baroness can permanently die on the battlefield in 4 days, if she is killed every 10 hours.
In the end, I think this system works fine. It is unlikely people will die as often as I cite above, but it gives us a good idea of what the maximum penalty would look like. People will need to be cautious in battle. Even rank-and-file soldiers will need to be careful, as they form (in-part) a protective barrier against the death of their leaders who are far more susceptible to permanent death on the battlefield.
EDIT: Changed rate for battlefield loss to 10 hours. Good catch, @Zirfith
This alters the number of days in battle to about 20 on the low end and less than 5 for officers and barons.
Apologies for the mistaken numbers.