Older hinges are invariably fitted with plain steel screws. These will be slowly (or rapidly) rusting away. The damper the wood, the quicker the rusting. They might have come loose in the past and been replaced with larger screws.

If using even larger screws is no longer an option to properly secure a hinge you’ll need to do a bit of remedial work on the frame or sash itself.

Or change the hinge for one with a different hole configuration. Or move the hinge.
My preferred option is to repair the wood. First drill out the screw hole with a drill bit size that will give you a good fit for a piece dowel. Glue in the piece of dowel. When cured, offer up the hinge, mark then drill a pilot hole for a new screw. Alternatively you can drill out and use a plastic "rawl" plug.

You need to use screws which are only used for window hinges. If you can, always use plated slot head screws. You might have found removing the hinge difficult because of all the paint over the screw heads. Just think how much harder this would have been if it was a cross head, pozidrive screw.

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