I think in some countries they are losing market share but not massively. I know here in the UK, a few issuers are now issuing American Express networked cards when they were previously MasterCards. Some issuers like Capital One stopped issuing Visa cards though and now only offer MasterCard, so its swings and roundabouts really.

Something MasterCard messed up on though was Debit cards. Most debits cards are either Visa and the ones that are MasterCard (Or Maestro) are often processed on a local debit network in the country of issue and actually only use MasterCard outside of the country.