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Definition of inexhaustible : Incapable of being exhausted, emptied, or used up; unfailing; not to be wasted or spent; as, inexhaustible stores of provisions; an inexhaustible stock of elegant words.

Synonyms:

forever, unflagging, renewable, unbroken, permanent, indefatigable, continuous, unfailing, active, outright, untiring, unceasing, tired, straight-out, never-ending, unsleeping, weariless, unwearied, continue, continuing, continual, tireless, indefinite

immemorial, unlimited, limitless, infinite, termless, eternal, bottomless, innumerable, everlasting, boundless, interminable, countless, illimitable, ceaseless, perpetual, timeless, unbounded, endless, numberless, incalculable, immeasurable

Usage examples:

• Millions of tons of ore have been taken from the mountains along the shore between Santiago and Guantanamo, and the supply appears to be inexhaustible. - "Cuba, Old and New", Albert Gardner Robinson.
• Those who had the honour to co- operate with His Royal Highness in the work to which I allude- and not a few are seated at this table- know by experience with what steadfast zeal and devotion and with what inexhaustible kindness in his dealings with all he carried it out; but no one, perhaps, so well as myself knows how desirous the Prince of Wales has been throughout that English Art should receive at the International Exhibition that recognition and honour which in his view it deserved, and which in the event was measured out to it by the opinion of Europe." - "Speeches and Addresses of H. R. H. the Prince of Wales: 1863-1888", Edward VII.
• His zeal knew no bounds, and his strength seemed inexhaustible. - "A Short History of Monks and Monasteries", Alfred Wesley Wishart.