Well, no, at a certain point (and indeed during normal market conditions, which right now isn't) there's an equilibrium. As global hashrate goes up, as you not, profitability goes down, which makes miners switch to other chains, or, eventually, power down their rigs.
I think your initial statement is correct, but from the wrong direction; if the ETH price is at 900$, the incentive to mine is less, some of current hashpower will already have left the mining of ETH, ergo OP is actually likely to still be profitable, although less so.
I didn't specify a direction, so I'm not sure how I can be describing the wrong one? My point is that the price of ethereum doesn't have to move at all and yet his mining rig will become unprofitable after a time. The hash rate will increase and/or more efficient miners will come online, leaving his equipment needing to mine faster or use less electricity in order to generate the same returns.
But, it's not a given that we'll have a significant enough increase of miners for that to be the case and time will tell (unless you happen to have knowledge I don't!)
I think your initial statement is correct, but from the wrong direction; if the ETH price is at 900$, the incentive to mine is less, some of current hashpower will already have left the mining of ETH, ergo OP is actually likely to still be profitable, although less so.