Suicide and honor
This will not be answer that was asked for. Instead, I will argue that the concept of honour worked in a way that suicide could not be an answer.
I will start by quoting Hávamál, verse 71:
The halt can manage a horse,
the handless a flock,
The deaf be a doughty fighter,
To be blind is better than to burn on a pyre:
There is nothing the dead can do.
Translation by W H Auden & P B Taylor
The Norse ideas of honour was not intrinsic: Honour was something you held in the eyes of others, and so was shame. You were not shamed by, for example, making a mistake. You were shamed if others treated you in a manner that indicated that you were not worthy of respect, or if you failed to demand the honour that should be due to you. If someone shamed you, the correct action would be to regain the honour in some way, typically by seeking revenge, or satisfaction through settlement or trial: any of these ways would prove that you were not someone to trifle with.
This, of course, means that suicide was generally not an acceptable way to redeem yourself, because it accomplishes nothing, or worse: it made you seem weak.
When revenge is impossible
Death might, however, be the result when revenge is impossible. Two good examples of this is Egill Skallagrímsson and Hrethel from Beowulf.
The cases are similar in that they are not "clear" suicides; in both cases it is more a case of a lost will to live after accidents have claimed their sons. What makes it interesting here is that in both cases this is connected to a matter of honour: Hrethel because his son has fallen to an arrow from his brother in an hunting accident, which cannot be avenged, Egil because his son has drowned, and as he says in Sonatorrek, he does not have the might to avenge himself on the ocean. Egill is eventually turned back to life by his daughter, while Hrethel dies:
Heartsore, wearied, he turned away,
from life's joys, choose God's light
and departed...
Beowulf, lines 2468-2470, translated by Seamus Heaney
Of course, this is rather obviously influenced by Christian thoughts, so it should be taken with some salt.
Suicide in battle
I will take an example from actual history: Olaf Tryggvason, who jumped ship when he realised that he had lost the battle of Svolder. This was, of course, in no way pre-mediated. Afterwards, all his remaining men also jumped ship. Snorri does not offer any judgement of this action.
Conclusion
Taking also the account of Brynhilde from Yannis answer into account, I would say that suicide in general was a result of grief, not shame. Shame was ideally to be washed away by gaining honour through great deeds, and killing yourself did not count.
Sources
- For the discussion of honor as a general concept, I have mostly relied on Gro Steinsland, Fornnordisk religion, even if some parts of it are my own: seh deos not specifically discuss suicide, for example. As far as I can tell, there are at least no contradictions.
- The analysis Of Egill and Hrethel is my own, even if there is not much interpretation needed: most of the stuff is explicitly spelled out.
- For Olaf Tryggvasson, I rely on Snorri's Heimskringla. From what I understand, the suicide is also covered by Adam of Bremen and Saxo Grammaticus.