Quick answer
A chain that loosens once or twice in its first hour of cutting is behaving normally. New chains seat into the sprocket and stretch through their first few heat cycles, and every manufacturer expects you to re-tension two or three times across the first tank of fuel or the first battery. A chain that keeps coming loose after break-in has a cause you can isolate in about ten minutes. In order of likelihood: tensioning technique, loose bar nuts, a worn drive sprocket, a worn bar, or a chain stretched past its adjustment range.
What correct tension looks like
Two checks, no tools. Pull the chain away from the bottom of the bar and let go: it should snap straight back against the rail. Then look at the underside of the bar: the drive links should sit fully in the groove with no visible droop. You should still be able to pull the chain around the bar with a gloved hand. If it won't move, it's over-tight, and that's its own problem. An over-tightened chain loads the bar rails and the motor bearings, and it gets tighter still as it cools.
Heat changes the measurement
Set tension cold. Ten minutes of cutting heats the chain enough that it will visibly sag, and that part is expected. The mistake is cranking a hot chain back to cold-spec tightness, because when it cools it contracts and clamps the bar. A chain tensioned while hot contracts as it cools, so slacken it after you finish work, as your manual directs.
The fix sequence, most likely first
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Re-tension with the bar nose held up. First shut off the engine or remove the battery, engage the chain brake, and wear gloves. Then loosen the bar nuts, lift the nose of the bar, set your tension, and tighten the nuts down while still holding the nose up. Letting the bar drop before the nuts are snug is the single most common technique fault, and it produces exactly this symptom: tight in the garage, loose after five cuts.
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Check the bar nuts themselves. Loose nuts let the bar shift under load, which dumps tension instantly. On saws with a tool-free tensioner, the big outer knob has to be cranked fully down after you set tension. Hand-snug backs off under vibration.
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Finish breaking in a new chain. Under an hour of cutting on the chain? Re-tension and keep working. Stretch tapers off sharply after the first few heat cycles, so this fixes itself.
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Inspect the drive sprocket. Take the chain off and look at the sprocket teeth. Deep wear grooves let the chain ride unevenly, and tension wanders no matter how carefully you set it. Oregon's rough rule of thumb is a new sprocket with every second chain, and most people are several chains past that.
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Inspect the bar. Burred rails, a widened groove, or a slight bend all let the chain wander and slap itself loose. File off rail burrs, flip the bar at every chain change to even out wear, and replace it once the groove is worn enough that the drive links bottom out.
When the chain is actually done
Every tensioner has a travel limit. If yours is at or near the end of its adjustment range and the chain still droops, the chain has stretched past its service life. Replace it. For a typical 16-inch homeowner saw that's a 91-series chain like the Oregon S56 with 56 drive links, but count your own drive links and match the pitch and gauge stamped on the bar, because "16 inch" alone doesn't guarantee fit.
Worth knowing for warranty purposes: chain stretch is normal wear, so no brand covers it. But a saw that eats a fresh chain despite correct tensioning, a good bar, and a good sprocket can have a faulty tensioner assembly, and that is a legitimate warranty claim on Ryobi, Ego, Milwaukee, and the rest.
The cause nobody checks: oil
A dry chain runs hot, and a hot chain stretches fast. Hold the saw firmly with the chain clear of everything, point the bar tip at a light surface such as cardboard, and run it briefly at part throttle with gloves and eye protection on; you should see a thin line of oil flick onto it. No line means the oiler port is clogged or the reservoir is empty. Clean the port where the bar meets the body, keep the tank topped with actual bar and chain oil, and a surprising number of chronic tension problems disappear.