I think the seed functions as a source of nutrients for small plants. I have a mango plant which didn't break out of shell completely (only shoot came out) and eventually its seed became rotten, maybe due to water accumulated in shell. And that plant is not growing like others and is very small but not dying though. Then maybe the seed help the baby plant to grow.
Normally the root (radicle) appears first, extends downwards and establishes a firm contact with the soil. Then the shoot appears with leaves. What can happen is the root begins growing but becomes tangled up in the shell and never finds a way out. This can be worse if the shell does not break open very much so there is little room for the radicle to emerge. In addition if the shell is planted on the soil so that the shell is not free draining then water can accumulate.
It sounds like one measure might be to break open the shell to see if there is any healthy root than can be encouraged to keep growing. The other thing is to accept it as a learning experience and try again with a new mango seed, perhaps by removing the seed from the shell before planting.