The question was aimed at @indy4x, but the problem with capacitors is that they don't always fail to 0uf. For example a 60uf capacitor can cause problems for a motor when the capacitance value drops, if it drops to 40uf the motor still may start but the current that the motor draws will increase, more current means more heat and the windings may suffer as a result. For me I tend to replace capacitors when the measured value is outside of the tolerance that is stated on the capacitor.
When I encounter a single phase motor that has started blowing fuses or tripping an overload the things I check are the supply voltage and the capacitor. I've recently seen someone trying to run a 230v motor from a supply with only 195v, and another where the overload was repeatedly reset, rather than find out what was causing the faults both motors are now big paper weights.
If it has two capacitors check if it has a centrifugal switch. These can stick and keep the start capacitor in circuit and can give the same symptoms as you have, ‘blows the fuse just as the motor gets up to speed’