The bottom rail is the lowest horizontal member of a window sash. On a box sash it is deeper than the other members, because it carries the weight of the glass, houses the joints into the stiles, and sits where water collects.
That last point is why it matters out of all proportion to its size. Rain runs down the glass and off the face of the sash onto the bottom rail, then stands there. On the outer face it meets the top of the sill, and if the two are in contact for long enough the joint stays wet through the winter. Almost every rotten sash starts here.
How the joints fail
The bottom rail is jointed into the stiles with a mortice and tenon, traditionally wedged and often pegged. Once water is in the timber the joint opens, the shoulders lose their bearing and the sash goes out of square. A sash that has dropped at one corner, binds against the frame, or shows an open line at the corner of the glass usually has a failed bottom rail joint rather than a problem with the cords.
Decay is frequently worse than it looks. Paint holds a convincing skin over timber that has gone soft beneath, so a rail that appears sound from the room can be spongy when probed from outside.
Repair or replace
A decayed bottom rail rarely justifies a new sash. The standard approach is to cut back to sound timber and splice in new material, matching species and grain direction, with the joint cut so that it is concealed when the sash is in place. The tenons are remade, the sash is re-wedged, and the whole is re-squared before it goes back into the frame.
This keeps the original glass, which is usually the most valuable thing about the window, and keeps the original stiles and their weathering. A replacement sash, however well made, replaces both. Where a rail is entirely gone a new one is made to the original section — the drip groove on the underside included, since leaving it out puts the next rail at risk.