There's lots of ways to do this. And it pretty much depends on exactly what you'd like to protect against for the major parts, and what you're connecting to for the details.
One way that would have helped here would have been network failsafe. basically the BigIP can monitor the attached vlans and if one of them goes 'down' the unit will go into standby. (In fact you can choose from standby, restart tmm, reboot etc).
However there's also ways to make sure that the networks themselves are more robust. You can do etherchannels (Trunks in F5 parlance) that can do LACP (802.1ad signalling that allows two interfaces to appear as one logical and be load-balanced for the traffic).
Or if LACP isn't available (e.g. two switches that usually won't do LACP across them - This is what you're really asking about above) you can simply have a spanned vlan across two switches and rely on STP (Spanning Tree) to stop the loop in the network. Careful design of your STP priorities is usually wanted to make sure the 'right' interfaces block (Usually you'd want one of the interfaces on the BigIP to be blocking).
** Note when I say spanning tree, what you usually want to run is called STP+ or PVST (Per VLAN Spanning Tree) which keeps a separate tree for each vlan. e.g. if you have two vlans you can block one on one interface and the second on the other interface.
H