Why is it that the bandwidth of a patch antenna decreases with it's size?
First of all L1 band ranges from 1563 MHz to 1587 MHz (Bandwidth = 24 MHz). 1590 MHz is falling in E1 which is GALILEO band.

In Layman's term: wavelength decreases with increase in frequency. 



In antenna theory, "for efficient radiation of electromagnetic energy the radiating antenna should be of the order of one-tenth or more the wavelength of signal radiated", which can be formulated as:

Size = λ/10, where λ is the wavelength

So as the frequency increases, wavelength decrease and thus the size of antenna.
Let's do the calculation for your case: (f=1590 MHz)

λ = c/f = 2.998*10^8 / 1590 * 10^6 = 0.18855 m = 18.855 cm ~ 19 cm

Size = λ/10 = 19/10 = 1.9 cm (which is quite small compared to standard 25 cm GPS patch antenna)

Further, in order to understand total relation between size, gain and bandwidth- theories calculations are mostly different from practical experience. This link provides good insight into the matter. Of course it is Chu–Harrington limit as suggested in primary comment.