During the bright outburst in 2011, the black hole candidate IGR J17091-3624 exhibited strong quasi-periodic flare-like events (on timescales of tens of seconds) in some characteristic states, the so-called heartbeat state. From the theoretical point of view, these oscillations may be modeled by the process of accretion disk instability, driven by the dominant radiation pressure and enhanced heating of the plasma. Although the mean accretion rate in this source is probably below the Eddington limit, the oscillations will still have large amplitudes. As the observations show, the source can exhibit strong wind outflow during the soft state. This wind may help to partially or even completely stabilize the heartbeat. Using our hydrodynamical code GLADIS, we modeled the evolution of an accretion disk responsible for X-ray emission of the source. We accounted for a variable wind outflow from the disk surface. We examined the data archive from the Chandra and XMM-Newton satellites to find the observed limitations on the wind physical properties, such as its velocity and ionization state. We also investigated the long-term evolution of this source, which lasted over about 600 days of observations, using the data collected by the Swift and RXTE satellites. During this long period, the oscillations pattern and the observable wind properties changed systematically. We found that this source probably exhibits observable outbursts of appropriate timescales and amplitudes as a result of the disk instability. Our model requires a substantial wind component to explain the proper variability pattern, and even complete suppression of flares in some states. The wind mass-loss rate extracted from the data agrees quantitatively well with our scenario.