What is the main challenge in the restart of a hypergolic upper stage, given that it does not require an igniter? Is it the difficulty in pushing propellent from tanks to the engine when the stage is experiencing zero acceleration? Or is it something else?
(Caveat: IANAE, but ...)
Ensuring that the engine doesn't have gas bubbles in the fuel/ox feed lines, and doesn't experience thrust transients; which might rip it apart; is a non-trivial problem. The LAM that they use for satellites operates with MMH and Nitrogen Tetroxide, IIRC, AND operates in a blow-down propulsion mode with Helium bottles providing the pressure. The (burpy) start provided by such a system might be OK at the lower thrust levels, and the smoother ramp up of an apogee motor for a satellite, but at the levels of thrust developed by a stage... you'd have to be concerned about RUD. So ISRO may've augmented the stage with (solid, monoprop, or even small bi-prop...although that seems unnecessarily complex) ullage motors, or modified the tankage to have those meshes and wicks that use capillary action and other surface tension effects (which strive to maintain a free surface), to ensure that the feed to the engines is smooth.
Furthermore, you'd have to maintain power to the final stage's flight computers (and the sensors) for ATLEAST the period of time between MECO and the second ignition. Satellites are power positive in that they GENERATE power. Not so for a rocket stage... so you'll have to add battery capacity. That means (non-payload) mass. You'd also probably want to maintain telemetry UPlink, in case you want to retain the option to command the stage remotely (for, what will be a very short lifetime - dictated by a mix of battery life time -- itself a function of thermal loads as you go in and out of orbital sunlight; and communication stations with the appropriate coverage).
Uplink (and downlink) AND power
could potentially be established by using the satellite's communication systems itself (i.e. without requiring additional batteries or telemetry antennae on the stage)... provided that there was an umbilical between the payload and the stage to allow a reverse transfer of power, and data. Given that the payload fairing would've already been jettisoned, the payload's antenna will likely be unshielded (unless it's mounted with its axis pointing INTO the stage); and the solar panels of the satellite could be deployed. HOWEVER, performing STAGE thrust manoeuvres with the solar arrays deployed would put those fragile structures under stresses that they're likely not designed to handle (and likely WON'T be designed to handle... because of the mass cost for a one-off use). So yeah, power and data communications capability of the stage would have to be upgraded; in addition to the propulsion tankage/ullage mechanisms.
EDIT: I did read the Zee News bit that Ohsin linked to in the previous post, but I'm a little unsure as to why it has to be cooled down. Sure, transient thrust spikes and concomitant mechanical and thermal stresses are all sorts of complex, and I can imagine that there's a very strict set of initial conditions required during the startup of the engine... and yes, thermal expansion and the geometry changes of the combustion chamber and the nozzle, as well as heat dissipation (when starting cold, as opposed to starting hot) during the startup will all be different... but my gut feeling is still scoffing at how an engine that can operate for 100s (say) and sustain the thermal loads for that long, will have a problem if it operates for 40s, takes a break, and comes back.
Anyway, I wonder if there's any kind of regenerative cooling that they're using this time round? Pumping the fuel through the nozzle, and mixing it with rest of the fuel - to aid this (and general) cooling down?