I haven't played Persia in a while, but doesn't Faith Healers make your Immortals truly immortal? In that they heal 100 points per turn if they are next to your city?
Actually, no, but there's enough misinformation about Faith Healers floating around the forums that I thought I would answer this question and address the misinformation.
First, post-Fall patch, the Immortal's "heals at double rate" promotion applies only to the regular +10 HP/turn healing rate that all units enjoy. It does not double the additional +10 HP from healing in friendly territory or the additional +5 HP from healing inside a city. It also does not double the +30 HP benefit from Faith Healers.
Second, Faith Healers requires that you be either inside the friendly city or immediately adjacent to the friendly city to get the healing benefit. The game designers mean what they say when they say "adjacent" (as with the Celtic UA requiring adjacent forests). Two tiles away is not good enough.
Since not everyone believes what they read in the forums, but may believe screenshots

, I fired up a quick Emperor game to generate some screenshots to demonstrate the truth about which I speak. Attached are screenies of
- an injured Immortal (20/100 HP),
- the Immortal after 1 turn of healing in friendly territory, but not adjacent to a friendly city (here, the capital) (+30 HP, consisting of the base +10 HP, doubled by the Immortal healing promotion, and +10 HP for healing in friendly territory),
- the Immortal healing adjacent to the city center (+60 HP, consisting of the regular friendly territory healing, and +30 HP from Faith Healers) and
- the Immortal healing inside the city (+65 HP, consisting of everything above, and +5 HP for healing inside the city).
As a total aside, this is a really forgiving Emperor map for anyone interested in moving up to Emperor and playing the Persians. I was just messing around (just wanted to generate and then heal my test Immortal), but the spawning site is behind a wall of mountains with only 2 passages, 4 unique luxuries and a bunch of resources, and I got the first pantheon (and wasted it on Faith Healers

) and Statue of Zeus (which I've never built - got the achievement for that one

); GL went on turn 54

. I've attached the initial save for anyone interested (sorry, all DLCs required).