It decreases with frequency at some point for all antennas, because there is always a frequency below which any antenna won't work. However, for most antennas there is also a frequency where the vswr will rise again. Most antennas have a band over which they are designed to work and in which the vswr is low, and it is high above and below this frequency band. The vswr may also be low at perhaps many other, usually higher, frequencies, where the antenna radiates, but not as designed.
Most people wouldn't want to use an antenna with a vswr worse than 10 anyway, as less than 1/3 of the power gets transmitted for vswr higher than this. Decent antennas have vswr less than 2, or 1.5, over their band of operation. Your antenna may be designed to work at about 5.5 GHz, beyond which the vswr rises again, and perhaps at around 6.7 Ghz. At vswr above 50, less than 7.7% of the power is radiated.
To give a precise answer of this question one would investigate the matching between the antenna impedance Za and that of the feeding line Zfl of the antenna with the frequency.
Assuming the mag. of the reflection coefficient is roh mag then the swr can be expressed by
swr= (1+ roh mag)/(1-roh mag),
roh = (Za- Zfl) / (Za+Zfl)
So we see that it depends on the matching between Za and Zfl and how they depend on the frequency.
So if the antenna is resonant and it is completely matched at its center frequency the the vswr as a function of frequency will appear as a band pass filter which is hinted by Malcolm White .
as already said above. by Malcolm et al...its a question of frequency dependent match..however your VSWR values are REALLY very high and only at a very few points more or less close to one. This is certainly not a nice broadband antenna.
I studied for long time electromagnetic Horn in circular and coaxial waveguide with perfect conducting walls for a frequancy range between 900Mhz to 110 Ghz for radio astronomic application .The truncated waveguide with thin walls in opend space has been studied using Wiener Hopf exact method and the reflection and transmission for each mode is given. For circular truncated waveguides we hav an optimum radius over wavelenght for wich the return losses are minimum but there is again increase and decreas that oscillates. . If you instead make use of a shaped flare to free space the return losses are low but again with oscilaltion due to diffraction. But at very high frquencies the waveguid wall present high corrugations with values that are comparable with wavelenght and the multimodal elements become propagative and the effect is again not constant but oscillates at anh modal new adition you have agin different behaviour.
The VSWR shown in the graph, if I'm reading the scale correctly, would indicate you have a terrible/useless antenna. A decent antenna would have a VSWR of less than 2:1, or 1.5:1. It will do this at, and near, its resonant frequency. VSWR values will be worse above and below that resonant frequency. Your graph is showing values of 50:1 or more (???) ...which would mean 95% or more of the power, sent to the antenna, is being reflected back to the source. So it is hardly acting as an antenna, at all (it is not accepting the power and radiating it into space). I personally find it easier to think in terms of Return Loss, rather than in VSWR. Return loss is in dB, and may be a little more intuitive; a VSWR of 2:1 would be a Return Loss of about 10dB, meaning 10% of the incident power to the antenna is being reflected back to the source. 1.5:1 would be about 14dB of RL. For reference, a commercial antenna for wireless communications (at the base station end, not the user end) will normally have a Return Loss of 14dB or better, within its band. A miniature antenna (inside a cell phone, for example) is usually too small to be naturally resonant, so it will be somewhat worse than this. A typical "whip" antenna, if it is the correct length, will also have an RL of around 10-14dB. Your "antenna" should be somewhere in this range, to really be considered a proper antenna.