In the framework of our narrow-band survey of the Local Group galaxies, we present the results of the search for planetary nebulae (PNe) in the dwarf irregular galaxies IC 10, Leo A and Sextans A. Using the standard on-band/off-band technique, sixteen new candidate PNe have been discovered in the closest starburst galaxy, IC 10. The optical size of this galaxy is estimated to be much larger than previously thought, considering the location of the new PNe in an area of 3.6 kpc x 2.7 kpc. We also confirm the results of previous studies for the other two dwarf irregular galaxies, with the detection of one candidate PN in Leo A and another one in Sextans A. We review the number of planetary nebulae discovered in the Local Group to date and their behaviour with metallicity. We suggest a possible fall in the observed number of PNe when [Fe/H] << -1.0, which might indicate that below this point the formation rate of PNe is much lower than for stellar populations of near Solar abundances. We also find non-negligible metallicity effects on the [O III] luminosity of the brightest PN of a galaxy. Based on observations obtained at the 2.5 m INT telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofisica de Canarias.