In my opinion, there's 3 primary factors. There's a difference between ice ages and ice age periods. The Milankovich cycles appear to play a key role in the forming and receding of individual ice ages, but what it doesn't appear to do is trigger ice age periods.
The modern Quaternary ice age period began about 2.58 million years ago. Milankovich cycles likely began long before then, so it's unlikely that Milankovich cycles triggered the period, only that they play a role in the cycle within the period.
Same is likely true for solar maximums and minimums. They come and go, but they aren't likely the drivers of ice age periods.
Timeline of glaciation
the Quaternary, the Karoo and the Andean-Saharan ice ages all happened in the last 450 million years, and they were separated by long periods so the cause should be looked at more long term. Milankovich cycles operate on 26,000, 42,000 and 100,000 timelines, much to short to drive changes over millions of years.
OK - the 3 things.
Land and ocean placement,
Solar output (long term, not short term sunspot changes), and
Land and Ocean Placement
One thing that seems necessary for ice age periods is a large land mass over one or both of the poles. The reason for this is pretty straight forward, land gives ice a place to grow and as land ice grows into a glacier, Albedo increases and oceans drop. High altitude over the glacier tends to blow cold air and maintain the glacier. Also as oceans cool, oceans can hold more CO2, dropping atmospheric CO2 and reducing the greenhouse effect. These feedback loops tend to make ice ages colder and they are only possible with land over one or both of the poles. Antarctica drifted over the South Pole and began forming a glacier about 30 million years ago and, in maybe 15-25 million years, it will drift off the the south pole and begin to melt. I think, once Antarctica drifts into warmer waters, ice ages are likely to stop. 15 million years or so? Maybe more?
It's also possible that Canada or Russia drift over the North Pole and as the the giant Antarctic Glacier is replaced by a giant Arctic Glacier, but I think the general consensus is that we can expect ice ages to stop when antarctic drifts over warmer water. We can also expect higher sea level too, lower Albedo and no more ice age cycle.
Solar output - long term, not short term sunspot cycles.
The sun growing more luminous, meaning, more energy for Earth, it's expected to grow warmer by about 10% over the next billion years - roughly 1% every 100 million years. (Source). 1% might not sound like much but it actually is. Solar variation, which is believed to have caused the Mini ice age, has a variation of about 1 - 1.5 watts per square meter. (Source)
A 1% more luminous sun would be in the range of 13-14 watts per square meter, so as the sun grows brighter, and if everything else stays the same, certainly within 100-200 million years, the sun would be sufficiently hot to make ice ages pretty darn unlikely. This site suggests that a 10% increase in solar luminosity could result in 47 °C, 116 °F. It will take quite a bit less than that to end ice ages. (Source)
We also have to consider orbital drift. If the Earth is slowly moving away from the sun, that's a factor too, and by this study, it is moving away, at 15 CM per year (Source), so, in 100 million years, 150,000 km, 0.1% further from the sun, about 0.2% less solar irradiance, which is only 20% of the increase in solar output,so this, at least by current estimates, will be overshadowed by the sun growing brighter. (Source)
Carbon Sequestering / atmospheric CO2 PPM
Finally, and very difficult to predict over the long term is carbon sequestering. CO2 has generally been decreasing over millions of years and the drop in CO2 may have played a role in the current ice age cycle. It's entirely possible, though some might disagree, but it's certainly possible that our current uptick in CO2 by human activity has already knocked the next ice age off it's feet and we might have changed the planet enough to end the ice age cycle. The orbital forcing is believed to be only about 1 degree C but ice ages can be about 10 degrees C colder due to feedback mechanisms. Our man made increase in CO2 is expected to warm the earth more than that, so at current CO2 levels, it's entirely possible that an ice-age couldn't form. source
The uncertainty in the estimates from various climate models for
doubling CO2-equivalent concentration is in the range of 1°C to 3°C
with the probability distributions having long tails out to much
larger temperature changes.
But, long term the CO2 isn't likely to stay at 400 PPM, though there's a good chance it won't drop to pre anthropomorphic levels of cycling between 180 and 280 PPM that we had during the recent ice age cycles. That might be enough to alter the recent ice age cycle, though long term predictions about CO2 sequestering are very difficult, but I do personally believe that by burning fossil fuels, we may have actually put an end to the ice age cycle. I'm by no means stating that as a certainty, but it's within the realm of possibility.
We've also seen CO2 levels gradually drop over millions of years, so it's possible, in a million or two years, we'll see CO2 levels even lower than we've seen and perhaps a resurgence of ice ages. Continental drift over the next few million years is predictable and solar output over longer periods is somewhat predictable, but CO2 sequestering is enormously difficult to predict - so that's the wild card in this estimate.
As we can see from the chart, there's been a pretty steady drop in CO2 PPM over the last 15 million years or so. As the ocean grows colder it can store more CO2 so there may be a correlation between falling temperature and falling CO2 PPM - one of the primary climate feedback mechanisms, but predicting future CO2 levels - I wouldn't even know what to guess. Certainly low enough CO2 PPM could lead to further ice ages, even after Antarctica drifts off the south pole, so, there's the problem - too many unknowns. This question has no answer.
A 4th possible key driver would be ocean currents, as indicated by the theory that the formation of the Isthmus of Panama may have been a key driver in the current ice age cycle, but predicting ocean current changes millions of years into the future is above my pay grade.
The 3 primary drivers do seem to fit past ice ages.
The the Andean-Saharan ice age period 425-450 million years ago, CO2 levels were much higher but that long ago the sun was perhaps 3%-4% less luminous and much of the land was over the antarctic circle.
The Karoo ice age period is associated with a drop in CO2 and an increase in O2 (Source)
That probably long and rambling and needs more than a little clean-up and I invite counterpoints, but I think that's the gist of estimating when ice ages will end. A precise answer isn't possible.