Which word is a better fit in the following sentence?
Some of the environmental changes may produce irreparable/irrecoverable damage to the earth's capacity to sustain life.
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M-W.com says this:
So they appear to be synonymous. Perhaps you can think of the difference in these two words this way:
I would use irreparable in your example sentence: Some of the environmental changes may produce irreparable damage to the earth's capacity to sustain life because the adjective modifies damage: once the damage is done, it cannot be undone. The earth's capacity to sustain life will be diminished, and that lost capacity cannot be recovered.
irreparable (OED: "Too far decayed to be repaired; past repair.") describes the level of damage something has sustained. It is damaged so extensively that it cannot be repaired in any way. A car could be irreparable.
irrecoverable (OED: "That cannot be recovered or got back: chiefly in reference to things lost.")describes loss, specifically the ability to revert to a previous state. Data on a hard-drive may be irrecoverable if it has been written over, but there is no sense of damage.
Irreparable and irrecoverable are not synonyms.
If the previously mentioned hard-drive has endured a fire and suffered irreparable damage, the data it contained is very likely irrecoverable, but note that irreparable describes the state of the hard-drive, while irrecoverable describes the state of the information.