No, it actually can't. Fire will burn as hot and quickly as it has fuel and oxygen to sustain, because it's a chemical reaction, it doesn't maintain any kind of steady-state in order to extend it's survival.
If you take away my food, I will still have energy to find more. If you take away my air, I will still have air (albeit quite time-limited) to find more. That gradient is how we understand something to be alive.
You can indeed argue it does maintain certain states to help extend its survival. Think of how fire tends to burn wood into charcoal. Now a big wind may blow out the primary flame, yet it actually lives on through the charcoal for a period of time, which when the right conditions are met, are able to reignite the blaze. Think of how fire tends to fragment matter, and send it up in the updraft. Sparks of this nature are able to ignite more fires further than the primary fire could reach on its own, beyond firebreaks even. This is akin to clonal propagation to ensure survival that we see in many species, or the release of many progeny over an area banking on the reality that most will not survive, but some will.
I think if we go further down the logic hole and start questioning that by virtue of it being something you can start yourself with a tinderbox, that fire is not life, we question the entire premise of ideas like abiogenesis which argue life is inevitable when certain chemical conditions being met.
> You can indeed argue it does maintain certain states to help extend its survival.
Not really. Everything you described is a property of chemistry and physics, not biology. Coals smolder under high residual heat and a lack of oxygen, not because of gated ion channels, osmotic barriers or any other evolved structure.
> This is akin to clonal propagation to ensure survival that we see in many species, or the release of many progeny over an area banking on the reality that most will not survive, but some will.
It's really not. Fire has no genome, nor a biological urge to reproduce. Cinders are a result of physics - pieces of organic matter fragment, heat causes rising air, some fragments are light enough to rise on hot air. If they are still hot when they land, fire can start at a new location.