Does anyone know under what conditions I would forfeit said opportunities?

If you have a "rollover IRA" that received only 401(k) money (other than earnings within the IRA itself), it can be rolled over into a new employer's 401(k) if the new employer's 401(k) allows it.

If you have a "rollover IRA" that received only 403(b) money (other than earnings within the IRA itself), it can be rolled over into a new employer's 403(b) if the new employer's 403(b) allows it.

If you mix 401(k) and 403(b) money in an IRA, that IRA cannot be rolled into a future employer's plan.

If you make any contributions (the $2,000/yr money) to a rollover IRA, that IRA cannot be rolled into a future employer's plan.

If the rollover IRA money is converted to Roth, that Roth money cannot be rolled into a future employer's plan. I don't know if converting part of a rollover IRA to Roth causes the remaining money to be unrollable into a future employer's plan.