In mapserver.h (row 1006) we can see the styleObj struct has offsetx and offsety. They are double.

mapserver.h

struct styleObj{
...
double offsetx, offsety; /* for shadows, hollow symbols, etc... */
...
}

According to this we can see in mapfile.c (row 2726 and 2736) they are treated as doubles when they are loaded in.

mapfile.c

int loadStyle(styleObj *style)
{
...
case(OFFSET):
if((symbol = getSymbol(2, MS_NUMBER,MS_BINDING)) == -1) return(MS_FAILURE);
if(symbol == MS_NUMBER)
style->offsetx = (double) msyynumber;
else {
...
if(symbol == MS_NUMBER)
style->offsety = (double) msyynumber;
else {
...
}

But in mapfile.c (row 2986) the style is saved by a writeDimension (mapfile.c row 525) function which wait ints on its 4th and 5th operands
that is why the OFFSET value of styleObj losts the precision of double when the map file is saved.

mapfile.c

...

static void writeDimension(FILE *stream, int indent, const char *name, int x, int y, char *bind_x, char *bind_y)
{
writeIndent(stream, ++indent);
if(bind_x) msIO_fprintf(stream, "%s [%s] ", name, bind_x);
else msIO_fprintf(stream, "%s %d ", name, x);
if(bind_y) msIO_fprintf(stream, "[%s]\n", bind_y);
else msIO_fprintf(stream, "%d\n", y);
}

...

void writeStyle(FILE *stream, int indent, styleObj *style)
{
...
writeDimension(stream, indent, "OFFSET", style->offsetx, style->offsety, style->bindings[MS_STYLE_BINDING_OFFSET_X].item, style->bindings[MS_STYLE_BINDING_OFFSET_Y].item);
...
}

The solution for this issue could be anther writeDimension function with 2 double operands.