Because the Arduino's input will "float" to an undefined value when there is no DC current path. Series capacitors block DC and the vibration sensor's built-in amplifier has a capacitor.
At a minimum you need a resistor-to-ground on the Arduino's analog input (10K or more should work).
And if you want to play it safe and protect the Arduino from negative voltages, use one of the circuits I suggested. The bias circuit puts the input at half the supply voltage and the other circuit puts the input at zero. (Then your vibration signal is added.)
If it works you should get "random looking" readings but you should be able to see the difference between small & large vibrations. Even with a large signal it's negative half of the time (ignoring any bias) and it crosses-through zero twice per cycle. But every cycle also has a positive & negative peak. Without any bias the negative half will read zero so about half of your readings should be zero.
Or if your readings are constantly too low you need an amplifier.
And you should take the delay out of your loop since you want to read it frequently.