Repeating more or less the same thing 3 times doesn't work for me in this poem. You could probably do more with this by expanding upon it some more.
The poem actually reminded me of a quote from Bladerunner which happens to be in my profile here on elite skills as well: These moments will be lost in time, like tears in the rain.
I'm not sure if you're trying to express something along those lines or something else, but you'll likely have to construct a good and clear juxtaposition for a poem like this to work well.
"There is silence - Once there was life. And I cry in the rain."
I don't think silence and crying go along well with eachother.
Where it has been burnt There is silence. The ash turns to mud, And [I] cry.
You just forgot to capitalize the "I" there... no big deal.
As for the rest, the content of the piece, I find that the metaphor does work when tied into the emotions felt. The symbology of ashes and mud and rain and tears is felt, however, I think as it stands now, the poem reads as a good footnote for something greater.
Instead of telling this in the tone of a short story, why not show more instead of explain? For example, instead of saying you cry, why not show through images that you're crying in juxtaposition with the rain? And instead of telling the audience what has been burnt and what that means, why not take us on a bit of a journey alongside with you, so we can sit back and interpret a little more?
You have some profound images lingering, and I think they'd be permanent images implanted in my mind if there was a bit more freedom in this piece. These are just my opinions, though. No need to change anything if you don't want to.