non-continuity in an 20 amp cartridge fuse for AC condenser unit
You don't mention the size of the breaker for the condenser circuit.  If the fuses are 20A and the breaker is 30A you'd obviously expect the fuses to blow first in an overload condition.  

If the fuses are 20A and the breaker is also 20A you'd still expect the fuses to blow before the breaker in an overload condition; generally fuses blow faster than breakers of the same rating in an overload.  

If the fuse is correct for the equipment and there was an overload that blew the fuse, it's possible your condenser is on the way out but it's also possible it was a one time glitch.  

Years ago a lot of condensers required fused disconnects but you don't see it in recent years.  Maybe your condenser is old, or maybe there are fuses there from an older unit that's been replace - if that's the case they may not be necessary at all (the breaker may be adequate without the supplemental fusing in the disconnect) or they may not be sized correctly, just left there from the old equipment.  

I'd have replaced both fuses (you now have one new one and one old one) and if it blows again, have the condenser serviced / checked.  I would not keep feeding it fuses indefinitely.  

(Fuses may seem old fashioned but fuses are still very reliable protection. 
 When they're old, maybe fuses may get a little faster to blow, but breakers can get a little slower, or may get a lot slower, or may not blow at all.  Old fuses may cause a nuisance but old breakers can be dangerous.)