Why is cytosine far more vulnerable to hydrolytic deamination than both adenosine and guanosine?
Cytosine deaminates to form uracil at a finite rate in vivo

Pyrimidine bases e.g cytosine in DNA are more susceptible to spontaneous deamination than are the purine bases because there are more thermolabile.


  This was demonstrated by the previous observation of significant
  cytosine deamination but no guanine deamination upon heating of the
  synthetic copolymer poly(dG-dC):poly(dG-dC) and the homopolymer
  poly(dG):poly(dC)


Reference: Journal of Biological Chemistry -  Nitric Oxide-induced Deamination of Cytosine and Guanine in Deoxynucleosides and Oligonucleotides

Another research article: Cytosine Deamination Plays a Primary Role in the Evolution of Mammalian Isochores agrees with the theory of temperature as the major cause of sponteneous demination in cytosine as it states:


  Because a 10°C increase in temperature in vitro increases the rate of
  cytosine deamination 5.7-fold, cytosine deamination must be highly
  dependent on body temperature.


Cytosine residues in DNA (2) can undergo hydrolytic deamination to yield uracil residues (3)

The reaction may proceed either via attack of hydroxide on the neutral nucleobase or attack of water on the N3-protonated base:




  In single-stranded DNA, and at base mismatches in duplex DNA,
  deamination proceeds much faster (t1/2 ~ 200 years) presumably due to
  increased solvent accessibility of the base.   Deamination of guanine
  and adenine residues in DNA is much slower, occurring at only 2–3% the
  rate of cytosine deamination.


Alkylation of the N3-position of cytosine and reactions that lead to saturation of the 5,6-double bond in cytosine and 5-methylcytosine accelerate deamination.

Activation-induced cytidine deaminases catalyse the conversion of cytosine residues to uracil residues in single-stranded regions of DNA.

Reference:  An Overview of Chemical Processes That Damage Cellular DNA: Spontaneous Hydrolysis, Alkylation, and Reactions with Radicals

Another factor which apparently "contributes" to susceptibilty of cytosine to hydroysis is its presence in both DNA and RNA. 

DNA is not susceptible to alkaline hydrolysis while RNA is alkali labile and is readily hydrolysed by hydroxide ions. On the other hand RNA is relatively resistant to the effects of dilute acid, but gentle treatment of DNA
with acid leads to hydrolysis of purine glycosidic bonds and the loss of
purine bases from the DNA.

These different conditions  (i.e acidic and basic conditions) to which the bases are exposed to appears to have a "double effect" on cytosine. (and additionally , as a pyrimidine it is more thermolabile)

Other reference


Biochemisty (Grisham)