First establish the following convention:
$$DutyCycle = \frac{SampleClockOnTime}{SampleClockPeriod}$$
In the following discussion,
$$SampleClockOnTime = T_p$$
$$SampleClockPeriod = T_s$$
You can model the effects of $T_p$ on your recovered signal as a pulse amplitude modulation signal recovery problem. The sample clock signal is a pulse with finite duty cycle. The reconstruction signal starts by modulating the sample clock signal with the data values of your sampled signal. Literally you can think of multiplying your samples values by a unit amplitude pulse (your sample clock) to create a physical time sequence.
In the frequency domain, you end up with a reconstructed signal that has altered frequency characteristics (roll off at the high frequencies) that are a direct consequence of the sample clock pulse width (aka duty cycle).
To complete the recovery of your signal, you will pass the modulated pulse signal through a low pass filter to obtain only the baseband components of the signal. The resulting signal with have frequency magnitude characteristis of the form:
$$|F'(f)| = |F(f)||\frac{T_psin(pifT_p)}{T_s*f*T_p}$$
Where:
F'(f) is the recovered signal and
F(f) is the spectrum of the origianl sampled signal
The effects of the sample clock pulse width is represented by:
$$\frac{T_psin(pifT_p)}{T_s*f*T_p}$$
If you plot this, you will see the amplitude rolls off as frequency approaches the sample clock frequency and the roll off is becomes more pronounced as $T_p$ increases.
You can look for more information on this by searching on the topic of "Sample and Hold effect". Most of the work I've seen on this topic is in the context of switched capacitor filters (which is how I was exposed to it).
