It is often stated that the magnetosphere not only shields the planet from cosmic radiation, but also prevents atmospheric loss. Why then did Venus not lose most of its atmosphere if it doesn't have a strong magnetic field? Is there another mechanism at play, or is the statement about the importance of magnetosphere to atmospheric loss prevention wrong?
There is an interesting article on the magnetosphere of Venus on the ESA Science and Technology site. You can find the article here and it will probably answer your question.
The article states, like you did, that some planets, like Earth, Mercury, Jupiter and Saturn, have magnetic fields internally induced by their iron core. These magnetic fields shield the atmosphere from particles coming from solar winds. It also confirms your statement that Venus lacks this intrinsic magnetosphere to shield its atmosphere from the solar winds.
The interesting thing, however, is that spacecraft observations, like the ones made by ESA's Venus Express, have shown that the Venusian ionosphere's direct interaction with the solar winds causes an externally induced magnetic field, which deflects the particles from the solar winds and protects the atmosphere from being blown away from the planet.
However, the article also explains that the Venusian magnetosphere is not as protective as Earth's magnetosphere. Measurements of the Venusian magnetic field show several similarities, such as deflection of the solar winds and the reconnections in the tail of the magnetosphere, causing plasma circulations in the magnetosphere. The differences might explain the fact that some gasses and water are lost from the Venus atmosphere. The magnetic field of Venus is about 10 times smaller than the earth's magnetic field. The shape of the magnetic field is also different. Earth has a more sharp magnetotail facing away from the Sun and Venus has a more comet-shaped magnetotail. During the reconnections most of the plasma is lost in the atmosphere.
The article explains therefore that although Venus does not have an intrinsic magnetic field, the interaction of the thick atmosphere with the solar winds causes an externally induced magnetic field, that deflects the particles of the solar winds. The article suggests, however, that the different magnetic field may mean that lighter gasses are not as protected and therefore are lost into space.
I hope this sufficiently answers the question.
There are other ways to lose atmosphere. For example Jean's Escape. If average velocity of a gas molecule exceeds escape velocity, the planet will lose atmosphere.
Venus' atmopshere is mostly $CO_2$ which has a higher molecular weight than the $0_2$ and $N_2$ of our atmosphere. So, for a given temperature and pressure, the carbon dioxide molecules have a slower speed. Venus' gravity is about the same as earth's and about twice Mars' gravity.
In summary, Venus' steep gravity well and massive gas molecules might be helpful in letting Venus hold on to an atmosphere.
A contributing factor to Venus' atmosphere is that Venus may still be geologically active. Any carbon dioxide emitted during volcanic eruptions will be adding to the atmosphere. If the rate of volcanic carbon dioxide emissions is greater than or equal to the rate of atmospheric loss Venus'atmosphere will be still be maintained.