I've gone back to the basics.  The keys seem to be to define the 
independent variable, to write both components of the vector field as 
functions but not to specify the inputs to the functions in the vector 
field definition, and (most critically) to use the parameter identifiers 
(ivar, dvars, time, ics) in the call to desolve_odeint.

The following code seems to be working now.

var('x y t')

def dx(x,y,t):
    if x<0.2:
        return(-x)
    else:
        return(y*(1-y))

def dy(x,y,t):
    return(1)

F=[dx,dy]

ans=desolve_odeint(F,ics=[0.5,1],times=srange(0,10,0.1),dvars=[x,y],ivar=t)
line(ans)


http://sagecell.sagemath.org/?z=eJxljUEKwjAQRfeF3iG7TmRaEsGNmG0vUYoEM5VATSGJJbm9qRZE_Kv5M483q_bQJJZZbHhd1ZWhiZkECTNGfq4rVmInli6iO-51i6f49A7axD87mgP9n_MBZJv5V5x_xTsm30CvBpPQ5HEr2gVlKCzzStfFkHURerS3oAbRnVCOGO2DggpeuzuBQClQdJKjWbUvUPkyoi2zisU9W0dQjPwF2u1AUQ==&lang=sage

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