There are lots of different ways to use sources in historical writing. That's why we go to graduate school for 4+ years. I don't know if it's entirely the case that historians give more credence to sources that were written immediately after or during whatever event we are looking at. Oral historians, for example, frequently interview people years or even decades after the event in question took place, and they can produce excellent work. One of the things they take into account, though, is that people can romanticize their or embellish their memories of events. A person writing years afterwards can perceive their involvement in events differently than it actually was. Even with sources written at the time, different historians can use them in different ways, with different specialties and goals in mind. Furthermore, someone involved in an historical event, such as a battle, is not going to see the whole thing. That person will only see his tiny piece of the battlefield. Even the commanding officer is not going to get a complete picture. That's one of the reasons why historians have to look at many different perspectives to try and get a clear idea of what happened. It's also why courts don't accept the word of a single witness. I think that the most important thing to remember is that we rarely or never completely assert that a single source is the complete truth. On some level, history is a science and we try and corroborate any source with a bunch of other sources.

The works on the Spanish Civil War written just after the war are generally considered to be too colored by the various writer's biases to be taken as the gospel truth. More recent histories such as the ones in this thread are usually the ones you'll see recommended. The authors' biases are more mild and the perspective is more sober. There has also been a recent (past 30 years) resurgence in oral histories and amazing archeological work that have enriched the field.

So, does the Spanish Civil War historian just disregard the earlier works? Heck no! Getting perspectives from the people who wrote while passions were still high is amazing. Want eight different passionate perspectives on an event during the war? No problem. Want what person X really thought about person Y? Likely not a problem either. Everyone venting their spleens in the aftermath of the Spanish Civil War is a gold mine. So, while I would recommend Thomas and Preston over Orwell and Aguirre for credibility, I wouldn't toss out the older works by a long shot.

I agree with a lot of what /u/onthefailboat has suggested here. For me, a source's value doesn't lie so much in its proximity to the event I'm studying as much as what it contributes to an array of historical knowledge about the event which I've been able to build up by considering it alongside the aggregate of other primary sources which also relate to the event. The proviso, though, is that these are all primary sources, which I would generally consider as being more relevant than interpretations offered in secondary sources, to also be consulted but not primarily.

Even then, though, when you're looking at all your primary sources together, you might notice that one source really sticks out; it might say something completely different than the others. Sometimes this new bit of info really aligns well with the rest of your knowledge about the source, but other times, just by virtue of your awareness of the historical context, you'll know that maybe a detail or two in a particular source is historically unlikely or inaccurate - after all, even if a source is written right after the event transpired, there can be some editorializing by its author. Even though they might not aid our reconstruction of the sequence of events, these extra nuggets are great for helping us understand how people at the time perceived what was happening.

I do community-based research, pairing oral history with archival research, so a big thing for me is to consider all primary sources I come across (and here I am also including non-conventional sources, like archaeological info, artwork, photography, etc) as being equally valid (see the Keough e-book at the bottom for a sense of what I mean here). This doesn't mean I treat everything I read as 100% accurate, but rather I approach oral history interviews as well as archival documents assuming that they each have the same likelihood of being accurate, though with an eye to the different benefits and drawbacks each source type offers. Ultimately, you have to assess each source on its own merits (there is still a debate about the viability of oral history, because there is a fear that our interview partners will misremember things that happened years earlier - however, we know that even people recording an event shortly after it happened do not accurately recall all of the details, so really, it behooves us to be critical of all sources as opposed to assuming that just because someone wrote something down that it will have been true).

Another point to make here, though, is that I emphatically don't think of myself as an objective "expert" distilling the one true narrative from primary sources. I'm the product of my society, upbringing, and training, and for sure all of those things influence my approach to history. Consider even historiography of Indigenous communities during the 1970s and 1980s. Those historians were working with many of the same primary sources some of us look at today, and yet they came to radically different conclusions than we accept today; ideas of a one-way model of cultural change where only Indigenous peoples' culture shifted after contact, a complete lack of analysis of the central role of Indigenous women in the fur trade, and even a perpetuation of salvage paradigm and vanishing Indian tropes (see Fisher, below). And yet, if we look to their practice, we can see that some of these historians also believed they were crafting objective narratives. The fault doesn't (always) lie within their analysis of primary sources, and certainly there was significant historical distance between themselves and their historical actors. Rather, part of the issue here is their failure to disclose precisely which epistemologies and intellectual traditions they were writing within. Definitely we should do the best we can, divulge our perspectives, and perhaps aim for neutrality, but IMO, objectivity isn't reachable.

Fisher, Robin. Contact and Conflict: Indian-European Relations in British Columbia, 1774-1890. Vancouver: UBC Press, 1977.

Keough, Willeen. The Slender Thread Irish Women on the Southern Avalon, 1750-1860. New York: Columbia University Press, 2008. (also published as an e-book by Gutenberg-e)