With fixed supply, compound growth in the economy translates to compound growth in the value of the currency.  To maintain the value of the subsidy as a constant, it must decline as the economy grows, and increase as the economy shrinks.  

A fixed subsidy will increase in value with economic growth, but decline as a portion of the economy, over time.  For example, in Monero, there will be about 18mm xmr circulating when subsidy is fixed at ~250k/an, according to the last proposal from core.  The first year that's ca1.4% VAT.  After 10 years it's ca. 1.2% VAT.

Whether the network is viable will depend on whether the tax is high enough to prevent growth/competitiveness, or low enough to prevent adequate funding of security. If mining goes to PoS the cost tends to zero.