One Titanian year spans over two complete solar cycles, and the solar irradiance has a significant effect on ionospheric densities. Solar cycle 24 has been one of the quietest cycles on record. In this paper we show data from the Cassini ion and neutral mass spectrometer (INMS) and the radio and plasma wave science Langmuir probe spanning the time period from early 2005, at the declining phase of solar cycle 23, to late 2015 at the declining phase of solar cycle 24. Densities of different ion species measured by the INMS show a consistent enhancement for high solar activity, particularly near the ionospheric peak. The density enhancement is best seen in primary ion species such as CH3+ rather than heavier ion species such as HCNH+. Unlike at Earth, where the ionosphere and atmosphere thermally expand at high solar activity, at Titan the altitude of the ionospheric peak decreases, indicating that the underlying neutral atmosphere was less extensive. Among the major ion species, CH5+ shows the largest decrease in peak altitude, whereas heavy ions such as C3H5+ show very little decrease. We also calculate the ion production rates using a theoretical model and a simple empirical model using INMS data and show that these effectively predict the increased ion production rates at high solar activity.