There are a few factors which confound an effort to find such an upper bound for grid size. Since these experiments normally require the rat to be attached to the recording apparatus to ensure the quality of the recorded data, the first obstacle would be perfecting the ability to record from the entorhinal cortex while the rat is untethered, through telemetry or bluetooth-enabled systems. Systems with enough throughput for the task are just becoming available (see here and here).
While the recording technology may be getting there slowly, in order to establish the periodicity of the grid cells, the rats must be trained to run around their environment using cues. In  the "polarity" of the bounded area was changed by rotating a white card in one corner. The grid cell activity is thus dependent on "allothetic" cues from the environment. Giving the rats carte blanche (forgive my pun) to roam around in a larger, less well defined area to test the scaling limits on grid cells might not provide enough constant visual cues to get a consistent grid map.
That's what we are not able know just yet, but what do we know?
In the rat it is known that the field spacing varies from 50 cm to 3 m depending on how far dorsal or ventral you are in the medial entorhinal cortex (within layer II). The average of the distance varied from 39-73 cm across different cells, though the standard deviation remains small (3.2 cm) . Spacing and field size got larger as you moved from the postrhinal border (from dorsal to ventral) ,. Stabilization of the measurements required at least some exposure to the experimental enclosure before measurements were taken.
In a rectangular area, the grid cells form a tiling of equilateral triangles, with the grid points at each mutual vertex. In , the spatial periodicity of the grids was tested by placing the rats on a track, rather than in an enclosure, controlling for one of the dimensions. This supports the above notion that to strengthen the knowledge about the grid cells, the focus has been on restricting the area of the experiment, rather than opening it up. From this study, it has been learned that the smallest scales are represented at the dorsal level, with the largest number of cells. Phase precession, a phenomenon in which spikes for a particular grid cell occurred later in the cycle of the theta wave at the center of the cell, and earlier upon entering the grid, was seen to decrease with the increasing field width. All of this together adds up to the idea that multiple spatial scales can all be held within this one layer of the entorhinal cortex, and scaled up and down as necessary using the precession to code for the specified representation.
In terms of other species, there have been studies in humans  (but limited to transit through virtual worlds, for the sake of fMRI recordings), mice, and piglets (though electrophysiology was not done). None of these studies have progressed beyond the initial stages.
So, much is known about the spacing characteristics of the grids themselves, but the upper limit of their spacing will have to wait for better experimental technology, and a clever design of a large experimental field that has consistent enough landmarks for the rats to incorporate into their grid representations.
 Hafting, T., Fyhn, M., et al (2005). Microstructure of a spatial map in the entorhinal cortex. Nature, 436:801-806.
 Brun, V.H., Solstad, T., et al (2008) Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus, 18:1200-1212.
 Doeller, C.F., Barry, C., Burgess, N. (2010). Evidence for grid cells in a human memory network. Nature, 463:657-661.